Bluebook SAT Test Right Triangles and Trigonometry 8

Question 1

In right triangle PQR with right angle at R, PQ = 29 and PR = 20. What is QR?

Accepted Answer

21

Answer

QR = √(29² − 20²) = √(841 − 400) = √441 = 21.

Question 2

In right triangle ABC with right angle at C, sin(B) = 7/25. What is cos(B)?

Accepted Answer

24/25

Answer

cos(B) = √(1 − 49/625) = √(576/625) = 24/25.

Question 3

A surveyor stands 80 feet from the base of a tower. The angle of elevation to the top of the tower is 45°. How tall is the tower?

Accepted Answer

80

Answer

tan(45°) = 1 = height/80; height = 80.

Question 4

A right triangle has legs of length 3k and 4k. If the hypotenuse is 50, what is k?

Accepted Answer

10

Answer

(3k)² + (4k)² = 25k² = 2500; k² = 100; k = 10.

Question 5

In a 45-45-90 triangle, angle A = 45° and the side opposite A is 6√2. What is the hypotenuse?

Accepted Answer

12

Answer

In a 45-45-90 triangle both legs are equal and the hypotenuse = leg × √2; leg = 6√2, so hyp = 6√2 × √2 = 12.

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