Bluebook SAT Test Right Triangles and Trigonometry 1

Question 1

A right triangle has legs of length 9 and 12. What is the length of the hypotenuse?

Accepted Answer

15

Answer

By the Pythagorean theorem: c² = 9² + 12² = 81 + 144 = 225, so c = 15.

Question 2

In right triangle ABC with the right angle at C, sin(A) = 3/5. What is cos(A)?

Accepted Answer

4/5

Answer

Since sin²(A) + cos²(A) = 1: cos(A) = √(1 − 9/25) = √(16/25) = 4/5.

Question 3

A 30-60-90 triangle has the shortest leg equal to 7. What is the length of the hypotenuse?

Accepted Answer

14

Answer

In a 30-60-90 triangle the hypotenuse is twice the shortest leg: 2 × 7 = 14.

Question 4

In right triangle PQR with the right angle at R, tan(P) = 5/12. If QR = 5, what is PR?

Accepted Answer

12

Answer

tan(P) = opposite/adjacent = QR/PR = 5/PR; solving, PR = 5 × 12/5 = 12.

Question 5

A ladder leans against a wall, making a 60° angle with the ground. If the ladder is 20 feet long, how high on the wall does it reach?

Accepted Answer

10√3

Answer

Height = 20 sin(60°) = 20 × (√3/2) = 10√3.

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