Bluebook SAT Test Right Triangles and Trigonometry 9 — Questions and Answers
Question 1: In right triangle ABC with the right angle at C, if sin(A) = 2/3, what is the value of sin²(A) + cos²(A)?
- 4/9
- 5/9
- 1 (Correct answer)
- 2/3
Correct answer: 1
The Pythagorean identity states sin²(θ) + cos²(θ) = 1 for any angle θ.
Question 2: A right triangle has legs of length 7 and 24. What is the value of sin of the angle opposite the leg of length 7?
- 7/24
- 24/25
- 7/25 (Correct answer)
- 24/7
Correct answer: 7/25
The hypotenuse is √(7² + 24²) = √(49 + 576) = √625 = 25, so sin = opposite/hypotenuse = 7/25.
Question 3: In a 30-60-90 right triangle, if the hypotenuse has length 8, what is the length of the side opposite the 60° angle?
- 4
- 4√3 (Correct answer)
- 8√3
- 4√2
Correct answer: 4√3
In a 30-60-90 triangle, the sides are in ratio 1 : √3 : 2, so the side opposite 60° = (8/2)·√3 = 4√3.
Question 4: Right triangle PQR has the right angle at R. If cos(P) = 5/13, what is tan(P)?
- 12/13
- 5/12
- 12/5 (Correct answer)
- 13/5
Correct answer: 12/5
If cos(P) = 5/13, then the adjacent leg is 5 and hypotenuse is 13, so the opposite leg is √(169 − 25) = 12, giving tan(P) = 12/5.
Question 5: A 10-foot ladder leans against a vertical wall. The base of the ladder is 6 feet from the wall. At what angle, to the nearest degree, does the ladder make with the ground?
- 37°
- 45°
- 53° (Correct answer)
- 60°
Correct answer: 53°
cos(θ) = 6/10 = 0.6, so θ = cos⁻¹(0.6) ≈ 53°.
Question 6: In right triangle ABC with right angle at C, AB = 10 and AC = 6. What is sin(B)?
- 3/5 (Correct answer)
- 4/5
- 3/4
- 4/3
Correct answer: 3/5
AC = 6 is adjacent to B, AB = 10 is the hypotenuse, so BC = √(100 − 36) = 8. sin(B) = opposite/hypotenuse = AC/AB = 6/10 = 3/5.
Question 7: Two right triangles are similar. The first has legs 6 and 8. The hypotenuse of the second triangle is 25. What is the perimeter of the second triangle?
- 50
- 55
- 60 (Correct answer)
- 75
Correct answer: 60
The first triangle has hypotenuse √(36+64) = 10. Scale factor = 25/10 = 2.5. Legs of the second = 6×2.5 = 15 and 8×2.5 = 20. Perimeter = 15 + 20 + 25 = 60.
Bluebook SAT Test Right Triangles and Trigonometry 9
In right triangle ABC with the right angle at C, if sin(A) = 2/3, what is the value of sin²(A) + cos²(A)?