Bluebook SAT Test Right Triangles and Trigonometry 6 — Questions and Answers
Question 1: A right triangle has legs of 20 and 21. What is the length of the hypotenuse?
- 29 (Correct answer)
- 30
- 28
- √841
Correct answer: 29
c = √(20² + 21²) = √(400 + 441) = √841 = 29.
Question 2: In right triangle ABC with right angle at C, sin(A) = 5/13. What is the length of AC if AB = 26?
- 24 (Correct answer)
- 10
- 12
- 20
Correct answer: 24
BC/AB = 5/13; BC = 10; AC = √(26² − 10²) = √(676 − 100) = √576 = 24.
Question 3: An observer stands 50 meters from a building. The angle of elevation to the roof is 60°. How tall is the building?
- 50√3 (Correct answer)
- 50/√3
- 100
- 25√3
Correct answer: 50√3
tan(60°) = √3 = height/50; height = 50√3.
Question 4: A 30-60-90 triangle has the longer leg = 12. What is the hypotenuse?
- 8√3 (Correct answer)
- 24/√3
- 24√3/3
- 8√3 · 2
Correct answer: 8√3
Shorter leg = 12/√3 = 4√3; hypotenuse = 2 × 4√3 = 8√3.
Question 5: In right triangle GHI with right angle at H, GH = 8 and GI = 17. What is cos(G)?
- 8/17 (Correct answer)
- 15/17
- 8/15
- 17/15
Correct answer: 8/17
cos(G) = adjacent/hypotenuse = GH/GI = 8/17.
Question 6: Two right triangles are similar with similarity ratio 2:5. If the perimeter of the smaller is 24, what is the perimeter of the larger?
- 60 (Correct answer)
- 48
- 120
- 30
Correct answer: 60
Perimeters scale linearly with the similarity ratio: 24 × (5/2) = 60.
Question 7: In right triangle ABC with right angle at C, angle A = 30° and BC = 4. What is the length of AB?
- 8 (Correct answer)
- 4√3
- 4√2
- 4/√3
Correct answer: 8
sin(30°) = BC/AB = 4/AB = 1/2; AB = 8.
Bluebook SAT Test Right Triangles and Trigonometry 6
A right triangle has legs of 20 and 21.
What is the length of the hypotenuse?