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Question

1)How do you find the length of the hypotenuse of a 45-45-90 triangle?


A. (leg)(√3)
B. The hypotenuse is equal to the length of the leg.
C. (leg)(√2)
D. (leg)(2)

2)How do you find the length of the long leg of a 30-60-90 triangle?


A. (short leg)(√3)
B. (short leg)(√2)
C. (short leg)(2)
D. (long leg)(√3)

3)ΔABC is a 30-60-90 triangle, with the right angle at A, 30° angle at B, and 60° angle at C. If BC = 4, what is the length of AB?

http://classroom.advancedacademics.com/coursecontent/Math/geom2004/GeomA_unit6/Unit6_Ch5_HW_files/image001.gif

A. 2
B. 2√3
C. 2√2
D. 8

Answer 1

How do you find the length of the Hypotenuse of a
45-45-90 Triangle

Pythagorean Theorem

c² = a² + b²

let

8 = length

√c² =√(8)² + (8)²

√c² = √64 + 64

√c² = √128

c = √128

c = √64√2

c = 8√2

The length of the hypotenuse is 8√2

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Sinθ = ab/bc

sin60° = ab/4

4sin60 = 4(ab/4)

4sin60 = ab

4(0.866025404) = ab

3.464101615 = ab

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The answer is b). 2√3



regentsprep.org/Regents/math/rtritrig/Ltri45.htm

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Answer 2

1)
leg square + leg square=hypotenuse square

C. (leg)(√2)


2)
A. (short leg)(√3)


3)
B. 2√3

Answer 3

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Answer 4

a square plus b square = c square
a and b are your legs and hypotenuse is your c
then at your last step u square root both sides