We would need to demonstrate that two angles of one triangle are congruent to two angles of the other triangle, and a pair of non-included sides are congruent.
To prove that triangles ΔXYZ and ΔFEG are congruent using the ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) congruence criteria, we need to show that they share certain corresponding angles and sides.
In ASA, we would need to show that both triangles have two congruent angles and the included side between those angles is congruent. In AAS, we would need to demonstrate that two angles of one triangle are congruent to two angles of the other triangle, and a pair of non-included sides are congruent.
Additional information that could be used to prove the congruence of ΔXYZ and ΔFEG using ASA or AAS includes:
1. Angle X = Angle F: If we can show that angle X in triangle ΔXYZ is congruent to angle F in triangle ΔFEG, we have one angle congruence.
2. Angle Y = Angle E: If we can demonstrate that angle Y in triangle ΔXYZ is congruent to angle E in triangle ΔFEG, we have the second angle congruence.
3. Side XY = Side FE: If we can prove that side XY in triangle ΔXYZ is congruent to side FE in triangle ΔFEG, we have the included side congruence.
Alternatively:
4. Angle Z = Angle G: If we can show that angle Z in triangle ΔXYZ is congruent to angle G in triangle ΔFEG, we have the second angle congruence in AAS.
5. Angle Y = Angle E: If we can demonstrate that angle Y in triangle ΔXYZ is congruent to angle E in triangle ΔFEG, we have the second angle congruence in AAS.
6. Side XZ = Side FG: If we can prove that side XZ in triangle ΔXYZ is congruent to side FG in triangle ΔFEG, we have a pair of non-included side congruence.
By establishing these angle and side congruences, we can use either the ASA or AAS congruence criteria to prove that triangles ΔXYZ and ΔFEG are congruent.
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If p1=(2,4,-3) and p=(3,-1,1) find parametric equation of
The parametric equation of the line passing through P1(2, 4, -3) and P(3, -1, 1) is:
x = 2 + t
y = 4 - 5t
z = -3 + 4t
To find the parametric equation of the line passing through points P1(2, 4, -3) and P(3, -1, 1), we can use the vector equation of a line.
Let's denote the direction vector of the line as d = (a, b, c). Since the line passes through P1 and P, the vector between these two points can be used as the direction vector.
d = P - P1 = (3, -1, 1) - (2, 4, -3) = (1, -5, 4)
Now, we can express the parametric equation of the line as follows:
x = x0 + at
y = y0 + bt
z = z0 + ct
where (x0, y0, z0) is a point on the line and (a, b, c) is the direction vector.
Let's choose P1(2, 4, -3) as the point on the line. Substituting the values, we get:
x = 2 + t
y = 4 - 5t
z = -3 + 4t
Therefore, the parametric equation of the line passing through P1(2, 4, -3) and P(3, -1, 1) is:
x = 2 + t
y = 4 - 5t
z = -3 + 4t
where t is a parameter that varies along the line.
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Find the zeros of the function shown below
Answer:
x = - 5 , x = 2
Step-by-step explanation:
f(x) = x² + 3x - 10
to find the zeros let f(x) = 0 , that is
x² + 3x - 10 = 0
consider the factors of the constant term (- 10) which sum to give the coefficient of the x- term (+ 3)
the factors are + 5 and - 2 , since
5 × - 2 = - 10 and 5 - 2 = + 3 , then
(x + 5)(x - 2) = 0 ← in factored form
equate each factor to zero and solve for x
x + 5 = 0 ( subtract 5 from both sides )
x = - 5
x - 2 = 0 ( add 2 to both sides )
x = 2
the zeros are x = - 5 , x = 2
Instructions: Complete the following proof by dragging and dropping the correct reason into the space provided.
Given: ∠NYR and ∠RYA form a linear pair, ∠AXY and ∠AXZ form a linear pair, ∠RYA≅∠AXY
If you are using a screen-reader, please consult your instructor for assistance.
Prove: ∠NYR≅∠AXY
Step Reason
∠NYR and ∠RYA form a linear pair
∠AXY and ∠AXZ form a linear pair Given
∠NYR and ∠RYA are supplementary
m∠NYR+m∠RYA=180
∠AXY and ∠AXZ are supplementary If two angles form a linear pair, then they are supplementary angles
Definition of Supplementary Angles
m∠NYR+m∠RYA=m∠AXY+m∠AXZ Substitution Property of Equality
∠RYA≅∠AXY
m∠NYR+m∠RYA=m∠AXY+m∠RYA Substitution Property of Equality
m∠NYR=m∠AXY
≅
Answer:
Step Reason
∠NYR and ∠RYA form a linear pair
∠AXY and ∠AXZ form a linear pair Given
∠RYA≅∠AXY Given
∠NYR and ∠RYA are supplementary Definition of Linear Pair
If two angles form a linear pair, then they are supplementary angles Definition of Linear Pair
∠NYR and ∠AXY are supplementary Transitive Property of Equality
m∠NYR+m∠RYA=180
m∠AXY+m∠AXZ=180 Definition of Supplementary Angles
m∠NYR+m∠RYA=m∠AXY+m∠AXZ Substitution Property of Equality
m∠NYR+m∠RYA=m∠NYR+m∠AXZ Substitution Property of Equality
m∠RYA=m∠AXZ Subtraction Property of Equality
∠NYR and ∠AXY are supplementary Definition of Supplementary Angles
m∠NYR+m∠AXY=180
m∠NYR+m∠RYA=m∠NYR+m∠AXY Substitution Property of Equality
m∠RYA=m∠AXY Subtraction Property of Equality
∠NYR≅∠AXY Definition of Congruent Angles.
Which of the following functions is graphed below ?
Answer:
A) [tex]\displaystyle y=\left \{ {{x^3-4,\,x\leq 1} \atop {x^2-3,\,x > 1}} \right.[/tex]
Step-by-step explanation:
The first "piece" of the piecewise function, [tex]y=x^3-4[/tex], contains [tex]x=1[/tex] because of the closed dot there.
The second "piece" of the piecewise function, [tex]y=x^2-3[/tex], doesn't contain [tex]x=1[/tex] because of the open dot there.
What occurs between the two pieces is called a jump discontinuity.
Therefore, A is the correct answer.
which graph represents this function
f(x)=1/2x-5
help would be appreciated
The graph of the equation f(x) = 1/2x - 5 is the graph (b)
How to determine the graph of the equationFrom the question, we have the following parameters that can be used in our computation:
f(x) = 1/2x - 5
The above expression is a linear equation that implies that
Slope = 1/2
y-intercept = -5
Next, we determine the graph
The graph that has a slope of 1/2 and y-intercept of -5 is (b)
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The physician’s order reads to administer Lasix 80 mg PO STAT. You have Lasix 20 mg tablets on hand. How many tablets will you administer to the patient ?
The nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.
To determine the number of Lasix 20 mg tablets that should be administered to the patient, we need to calculate how many tablets are equivalent to the prescribed dose of 80 mg.
Given that each Lasix tablet contains 20 mg of the medication, we can divide the prescribed dose (80 mg) by the dosage strength of each tablet (20 mg) to find the number of tablets needed.
Number of tablets = Prescribed dose / Dosage strength per tablet
Number of tablets = 80 mg / 20 mg
Number of tablets = 4 tablets
Therefore, the nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.
It is important to note that this calculation assumes that the Lasix tablets can be divided or split if necessary. However, it is crucial to follow the specific instructions provided by the prescribing physician or consult with a pharmacist if there are any concerns about the appropriate administration of the medication.
Additionally, it is important to consider any additional instructions, such as the frequency and timing of administration, as specified by the physician's order.
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the peterson family and the stewart family each used their sprinklers last summer. the water output rate for the peterson family’s sprinkler was 35 L per hour. the water output rate for the stewart family’s sprinkler was 40 L per hour. the families used their sprinklers for a combined total of 45 hours, resulting in a total water output of 1,650 L. how long was each sprinkler used?
The Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.
Let's assume that the Peterson family used their sprinkler for a certain number of hours, which we'll denote as x, and the Stewart family used their sprinkler for the remaining hours, which would be 45 - x.
The water output rate for the Peterson family's sprinkler is given as 35 L per hour. Therefore, the total water output for the Peterson family can be calculated by multiplying the water output rate (35 L/h) by the number of hours they used the sprinkler (x): 35x.
Similarly, for the Stewart family, with a water output rate of 40 L per hour, the total water output for their sprinkler is given by 40(45 - x).
According to the problem, the combined total water output for both families is 1,650 L. Therefore, we can write the equation:
35x + 40(45 - x) = 1,650.
Simplifying the equation, we get:
35x + 1,800 - 40x = 1,650,
-5x = 1,650 - 1,800,
-5x = -150.
Dividing both sides of the equation by -5, we find:
x = -150 / -5 = 30.
So, the Peterson family used their sprinkler for 30 hours, and the Stewart family used theirs for 45 - 30 = 15 hours.
Therefore, the Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.
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What number completes the sequence below? Enter your answer in the input
box at the bottom.
8————-4
16————8
24———-12
32———-?
Answer here
Answer:
The number is 16
Step-by-step explanation:
This follows a multiplication rule,
4 times 1 = 4
4 times 2 = 8
4 times 3 = 12
4 times 4 = 16
So, the number is 16
Sin(theta)=2/3 and theta is in quadrant II, find cos theta
Answer: Choice C. [tex]\displaystyle \boldsymbol{-\frac{\sqrt{5}}{3}}[/tex]
===================================================
Work Shown:
Part 1
[tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\\cos^2(\theta) = 1-\sin^2(\theta)\\\\\cos(\theta) = -\sqrt{1-\sin^2(\theta)} \ \ \text{ ..... cosine is negative in Q2}\\\\\cos(\theta) = -\sqrt{1-\left(\frac{2}{3}\right)^2}\\\\\\cos(\theta) = -\sqrt{1-\frac{4}{9}}\\\\[/tex]
Part 2
[tex]\cos(\theta) = -\sqrt{\frac{9}{9}-\frac{4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{9-4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{5}{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{\sqrt{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{3}\\\\[/tex]
If 2x2 - 4x + 6 = 1 then A = 2, B = -4, and C = 6 in general form.
In general form, the equation 2x^2 - 4x + 6 = 1 can be represented as A = 2, B = -4, and C = 5.
To determine the values of A, B, and C in the general form of the quadratic equation 2x^2 - 4x + 6 = 1, we can compare the given equation with the standard form of a quadratic equation, which is ax^2 + bx + c = 0.
In the given equation, we have:
2x^2 - 4x + 6 = 1
To put it in the general form, we need to move all the terms to the left side of the equation, so the right side is equal to 0:
2x^2 - 4x + 6 - 1 = 0
2x^2 - 4x + 5 = 0
Now we can identify the coefficients A, B, and C in the general form:
A = 2 (coefficient of x^2)
B = -4 (coefficient of x)
C = 5 (constant term)
The values of A, B, and C in the general form of the equation 2x^2 - 4x + 6 = 1 are A = 2, B = -4, and C = 5.
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What is the volume of this
figure?
A 774 cm³
B 3,546 cm³
C 843 cm3
D 2,250 cm³
Hello!
Volume
= (18cm * 15cm * 6cm) + ((13cm - 6cm) * 15cm * 6cm)
= 1,620cm³ + 630cm³
= 2,250cm³
If is an acute angle and =35 then =?
Answer:
A acute angle is a angle that is less than 90*
Printing orders for Magma printers arrive at an average rate of 5 orders per hour. Assume these
orders follow a Poisson distribution.
(a) Calculate the probability that exactly 4 orders will arrive in 30 minutes? (4)
(b) Determine the probability that at least 2 orders will arrive in an hour?
Answer:
Step-by-step explanation:
To solve these problems, we can use the Poisson probability formula:
P(x; λ) = (e^(-λ) * λ^x) / x!
Where:
P(x; λ) is the probability of x events occurring
e is the base of the natural logarithm (approximately 2.71828)
λ is the average rate of events occurring in the given time period
x is the number of events
(a) Probability of exactly 4 orders arriving in 30 minutes:
The average rate of orders is given as 5 orders per hour. To find the average rate of orders in 30 minutes, we divide it by 2 (since 30 minutes is half an hour):
λ = 5 orders/hour / 2 = 2.5 orders/30 minutes
Using the Poisson probability formula:
P(x = 4; λ = 2.5) = (e^(-2.5) * 2.5^4) / 4!
Calculating this:
P(x = 4; λ = 2.5) ≈ (0.082 * 39.0625) / 24
P(x = 4; λ = 2.5) ≈ 3.22265625 / 24
P(x = 4; λ = 2.5) ≈ 0.134
Therefore, the probability that exactly 4 orders will arrive in 30 minutes is approximately 0.134, or 13.4%.
(b) Probability of at least 2 orders arriving in an hour:
To find the probability of at least 2 orders, we need to calculate the probabilities of having 0 and 1 order and subtract it from 1 (since it's the complement).
Using the Poisson probability formula:
P(x = 0; λ = 5) = (e^(-5) * 5^0) / 0! = e^(-5) ≈ 0.0067
P(x = 1; λ = 5) = (e^(-5) * 5^1) / 1! ≈ 0.0337
P(at least 2 orders) = 1 - P(x = 0) - P(x = 1) ≈ 1 - 0.0067 - 0.0337 ≈ 0.9596
Therefore, the probability of at least 2 orders arriving in an hour is approximately 0.9596, or 95.96%.
Which property best describes the conditional statement below If triangle ABC= triangle DEF then triangle DEF=triangleABC
Answer:
would this not be a converse statement?
Step-by-step explanation:
triangle ABC is the hypothesis and it's conclusion is triangle DEF
Jane just joined a group that makes hats for babies in the hospital. Two weeks ago they made 21 hats. Last week they made 29 hats. This week they made 12 hats. All these hats will be split evenly between 2 nearby hospitals. Jane works out that's 62 hats for each hospital. Does that sound about right?
Answer:
31
Step-by-step explanation:
you add the hats to get the total number of hats then divide the answer by
No, it is much too high. Then the correct option is B.
What is an equation?An equation is a statement of equality between two expressions consisting of variables and/or numbers.
Given the question above, we need to find if the hats is to high or low.
Calculating the total numbers of hats made, we have
[tex]21 + 29 + 12 = 62 \ \text{hats}[/tex]
If Edna wants to split 62 hats evenly between two hospital, then each hospital will get
[tex]\dfrac{62}{2} = 31 \ \text{hats}[/tex]
Therefore, if Edna works out that each hospital gets 62 hats, No it is too high, as that is the total of all the hat that is available
Hence, the correct option is B.
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Missing informationEdna just joined a group that makes hats for babies in the hospital. Two weeks ago they made 21 hats. Last week they made 29 hats. This week they made 12 hats. All these hats will be split evenly between 2 nearby hospitals. Edna works out that's 62 hats for each hospital. Does that sound about right?
A. Yes
B. No, it is much too high
C. No, it is much too low
GEOMETRY 80POINTS
ty!
Answer:
x ≈ 77.79 ft
Step-by-step explanation:
using the sine ratio in the right triangle
sin40° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{50}{x}[/tex] ( multiply both sides by x )
x × sin40° = 50 ( divide both sides by sin40° )
x = [tex]\frac{50}{sin40}[/tex] ≈ 77.79 ft ( to the nearest hundredth )
PLEASE HELP! EXPLAIN THOROUGHLY EACH QUESTION SHOULD BE ANSWERED IN A 2 SENTENCE EXPLINATION AND I WILL MARK IT BRAINLIEST!
7.
This figure shows a quadrilateral made of triangle ABF
and triangle DEC
.
a. What does it mean for triangles to be congruent?
b. Jane is told that angle A
is congruent to angle D
and angle B
is congruent to angle E
She concludes that the triangles are congruent because of AAA. Explain why she thinks this, and whether or not you think she is right.
c. George is told the same thing as Jane, but he concludes that the triangles are congruent because of ASA. Explain why he thinks this, and whether or not you think he is right.
d. Are there any other ways the two triangles could be congruent with the information Jane and George have been given? Explain why you think this.
The required answers of the given questions are answered below.
a), b), c), d)
What is quadrilateral?A quadrilateral is geometric structure enclosed in 4 sides.
A) Because,
1) the angle A = Angle D
2) its has a common side
3) the angle D = Angle B
∵ ΔEAB ≅ EDC
Thus, Both the triangle is congruent by ASA.
B.)
Jane conclusion is also write for AAA
because by angle E is congruent to angle B, implies angle F is congruent to angle C.
So that is why Jane conclude AAA.
C.) George conclusion is also perfect
George thinks the following conditions-
1) the angle A = Angle D
2) its has a common side
3) the angle D = Angle B
∵ ΔEAB ≅ EDC
Thus, Both the triangle is congruent.
Hence, Both the triangles are congruent by SSS.
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what is the square root of the fraction, 3/25?
Answer: 0.3464 (correct upto 4 decimal places )
Step-by-step explanation:
[tex]\sqrt{3/25}[/tex]= [tex]\sqrt{3} /\sqrt{25\\}[/tex] (as the square root of 25 is 5)
=1.73205/5
=0.3464
find the value x, round the lengths of segments to nearest tenth and the measure of angles to the nearest degree
Answer:
Step-by-step explanation:
39 !!!!!
In circle I, IJ = 9 and m/JIK = 140°. Find the length of JK. Express your answer as a fraction times pie.
The calculated length of the arc JK is 7π
Finding the length of the arc JKFrom the question, we have the following parameters that can be used in our computation:
Central angle = 140 degrees
Radius, IJ = 9 inches
Using the above as a guide, we have the following:
JK = Central angle/360 * 2 * π * Radius
Substitute the known values in the above equation, so, we have the following representation
JK = 140/360 * 2 * π * 9
Evaluate
JK = 7π
Hence, the length of the arc is 7π
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3. Determine whether the triangles are similar. If they are, write a similarity statement.
Look at picture for reference
Please show work
The triangles DEF and SRQ are not similar triangles
Identifying the similar triangles in the figure.From the question, we have the following parameters that can be used in our computation:
The triangles in this figure are
DEF and SRQ
These triangles are not similar
This is because:
The corresponding angles in the triangles are not equal
For DEF, the angles are
50, 90 and 40
For SRQ, the angles are
51, 90 and 39
This means that they are not similar by any similarity statement
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In circle P with m LN RQ = 60, find the
m/NPQ.
Answer:
∠ NPQ = 120°
Step-by-step explanation:
the central angle NPQ is twice the angle on the circle NRQ , subtended by the same arc NQ , then
∠ NPQ = 2 × 60° = 120°
The base of a rectangular prism is a square whose sides each measure 9 inches. The height of the rectangular prism is 11 inches, find it’s volume?
Answer:
99
Step-by-step explanation:
since the height is 9 and the base is 11 we use the formula BH=V
substitute 9x11 and get 99
Determine the perimeter of a soccer field with a length of 97 metres and a width of 69 metres
Answer: Therefore, the perimeter of the soccer field is 332 meters.
Step-by-step explanation:
To determine the perimeter of a soccer field with a length of 97 meters and a width of 69 meters, we can use the formula for the perimeter of a rectangle, which is given by:
Perimeter = 2 * (length + width)
Plugging in the values, we have:
Perimeter = 2 * (97 + 69)
Perimeter = 2 * 166
Perimeter = 332 meters
Write the equation of the trigonometric graph.
Answer:
[tex]y=\boxed{2}\:\cos \left(\boxed{1}\;x\right)+\boxed{3}[/tex]
Step-by-step explanation:
The graph of the solid black line is the cosine parent function, y = cos(x).
The standard form of a cosine function is:
[tex]\boxed{y = A \cos(B(x + C)) + D}[/tex]
where:
A is the amplitude (height from the mid-line to the peak).2π/B is the period (horizontal distance between consecutive peaks).C is the phase shift (horizontal shift - positive is to the left).D is the vertical shift (the mid-line is y = D).From inspection of the graph, the x-values of the turning points (peaks and troughs) of the parent function and the new function are the same. Therefore, the period of both functions is the same, and there has been no horizontal shift. So, B = 1 and C = 0.
The mid-line of the new function is y = 3. Therefore, D = 3.
The y-value of the peaks is y = 5. The amplitude is the distance from the mid-line to the peak. Therefore, A = 2.
Substituting these values into the standard formula we get:
[tex]y = 2 \cos(1(x + 0)) + 3[/tex]
[tex]y=2 \cos (1(x))+3[/tex]
[tex]y= 2 \cos(x) + 3[/tex]
Therefore, the equation of the trigonometric graph is:
[tex]y=\boxed{2}\:\cos \left(\boxed{1}\;x\right)+\boxed{3}[/tex]
Given the calculator output below, determine the following: (round all answers to four decimal places)
LinReg
y=ax+b
a=.1186440678
b=3.677966102
r2=.0353407862
r. 1879914523
a.) What is the value of the correlation coefficient?
b.) What is the value of the slope of the regression line?
c.) What is the value of the coefficient of determination?
d.) What is the value of the y-intercept of the regression line?
Answer:
a) r = .1880
b) a = .1186
c) r² = .0353
d) b = 3.6780
A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. What is the maximum area of a Norman window whose perimeter is 9 feet?
The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.
To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:
πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:
A = (πr^2)/2 + rh
To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:
r = (9 - 2h)/(π)
Now we can rewrite the area function in terms of h only:
A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)
Simplifying this equation, we get:
A = (1/2)(9h - h^2/π)
To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:
dA/dh = 9/2 - h/π = 0
Solving this equation, we find:h = 9π/2
Substituting this value of h back into the area function, we get:
A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4
Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.
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Input an ordered pair that satisfies the system of inequalities:
-
y < − x − 3
y> 2x - 4
To find an ordered pair that satisfies the given system of inequalities, we need to find a point that lies below the line y = -x - 3 and above the line y = 2x - 4.
One such point that satisfies both inequalities is (-1, 0).
Let's check if this point satisfies both inequalities:
For the first inequality, y < -x - 3:
0 < -(-1) - 3
0 < 1 - 3
0 < -2 (True)
For the second inequality, y > 2x - 4:
0 > 2(-1) - 4
0 > -2 - 4
0 > -6 (True)
Therefore, the ordered pair (-1, 0) satisfies the system of inequalities y < -x - 3 and y > 2x - 4.
priya and han each wrote an equation of a line with slope 1/3 that passes through the point (1,2). priyas equation is y - 2 = 1/3 (x-1) and hans equation is 3y-x=5. do you agree with either of them? explain or show your reasoning
I agree with both Priya's and Han's equations.
To determine if either Priya or Han equation is correct, we can substitute the coordinates of the given point (1,2) into each equation and check if the equation holds true.
For Priya's equation, y - 2 = (1/3)(x - 1), substituting x = 1 and y = 2:
2 - 2 = (1/3)(1 - 1)
0 = 0
The equation holds true, so Priya's equation is correct.
For Han's equation, 3y - x = 5, substituting x = 1 and y = 2:
3(2) - 1 = 5
6 - 1 = 5
5 = 5
The equation also holds true, so Han's equation is correct.
Both Priya's and Han's equations are valid equations of the line with a slope of 1/3 passing through the point (1,2). The equations have different forms, but they are algebraically equivalent and represent the same line. Therefore, I agree with both Priya's and Han's equations.
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special right triangle