Bluebook SAT Test Right Triangles and Trigonometry 2

Question 1

In right triangle ABC with the right angle at C, AB = 17 and BC = 8. What is the value of tan(A)?

Accepted Answer

8/15

Answer

AC = √(17² − 8²) = √(289 − 64) = √225 = 15; tan(A) = opposite/adjacent = BC/AC = 8/15.

Question 2

A right triangle has a hypotenuse of 26 and one leg of 10. What is the length of the other leg?

Accepted Answer

24

Answer

Other leg = √(26² − 10²) = √(676 − 100) = √576 = 24.

Question 3

A ramp rises 5 feet over a horizontal distance of 12 feet. What is the length of the ramp?

Accepted Answer

13

Answer

Ramp length = √(5² + 12²) = √(25 + 144) = √169 = 13.

Question 4

In a right triangle, one acute angle measures 30°. The side opposite this angle is 7. What is the length of the hypotenuse?

Accepted Answer

14

Answer

sin(30°) = 1/2 = opposite/hypotenuse = 7/hyp; hyp = 14.

Question 5

A 45-45-90 triangle has legs of length 9. What is the perimeter of the triangle?

Accepted Answer

18 + 9√2

Answer

Hypotenuse = 9√2; perimeter = 9 + 9 + 9√2 = 18 + 9√2.

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