Bluebook SAT Test Right Triangles and Trigonometry 8 — Questions and Answers
Question 1: In right triangle PQR with right angle at R, PQ = 29 and PR = 20. What is QR?
- 21 (Correct answer)
- 22
- 19
- √441
Correct answer: 21
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)?
- 24/25 (Correct answer)
- 7/24
- 25/24
- 25/7
Correct answer: 24/25
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?
- 80 (Correct answer)
- 80√2
- 40√2
- 160
Correct answer: 80
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?
- 10 (Correct answer)
- 5
- 8
- 12
Correct answer: 10
(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?
- 12 (Correct answer)
- 6
- 6√2
- 12√2
Correct answer: 12
In a 45-45-90 triangle both legs are equal and the hypotenuse = leg × √2; leg = 6√2, so hyp = 6√2 × √2 = 12.
Question 6: Right triangles P and Q are similar. Triangle P has legs 8 and 15. Triangle Q has the longer leg equal to 45. What is the hypotenuse of Triangle Q?
- 51 (Correct answer)
- 45
- 30
- 24
Correct answer: 51
Scale factor = 45/15 = 3; Triangle P hypotenuse = 17; Triangle Q hypotenuse = 17 × 3 = 51.
Question 7: In right triangle ABC with right angle at C, angle A = 60° and AC = 5. What is BC?
- 5√3 (Correct answer)
- 10
- 5/√3
- 5√2
Correct answer: 5√3
tan(60°) = √3 = BC/AC = BC/5; BC = 5√3.
Bluebook SAT Test Right Triangles and Trigonometry 8
In right triangle PQR with right angle at R, PQ = 29 and PR = 20.
What is QR?