Bluebook SAT Test Right Triangles and Trigonometry 2 — Questions and Answers
Question 1: In right triangle ABC with the right angle at C, AB = 17 and BC = 8. What is the value of tan(A)?
- 8/15 (Correct answer)
- 15/8
- 8/17
- 15/17
Correct answer: 8/15
AC = √(17² − 8²) = √(289 − 64) = √225 = 15; tan(A) = opposite/adjacent = BC/AC = 8/15.
Question 2: A right triangle has a hypotenuse of 26 and one leg of 10. What is the length of the other leg?
- 24 (Correct answer)
- 20
- 16
- 28
Correct answer: 24
Other leg = √(26² − 10²) = √(676 − 100) = √576 = 24.
Question 3: A ramp rises 5 feet over a horizontal distance of 12 feet. What is the length of the ramp?
- 13 (Correct answer)
- 17
- 15
- 11
Correct answer: 13
Ramp length = √(5² + 12²) = √(25 + 144) = √169 = 13.
Question 4: In a right triangle, one acute angle measures 30°. The side opposite this angle is 7. What is the length of the hypotenuse?
- 14 (Correct answer)
- 7√3
- 7√2
- 7
Correct answer: 14
sin(30°) = 1/2 = opposite/hypotenuse = 7/hyp; hyp = 14.
Question 5: A 45-45-90 triangle has legs of length 9. What is the perimeter of the triangle?
- 18 + 9√2 (Correct answer)
- 27
- 18
- 9 + 18√2
Correct answer: 18 + 9√2
Hypotenuse = 9√2; perimeter = 9 + 9 + 9√2 = 18 + 9√2.
Question 6: In right triangle XYZ with the right angle at Z, cos(X) = 5/13. What is sin(X)?
- 12/13 (Correct answer)
- 5/12
- 13/12
- 13/5
Correct answer: 12/13
sin²(X) + cos²(X) = 1; sin(X) = √(1 − 25/169) = √(144/169) = 12/13.
Question 7: Two similar right triangles have corresponding hypotenuses of 10 and 25. If the shorter triangle has a leg of 6, what is the corresponding leg of the larger triangle?
- 15 (Correct answer)
- 12
- 10
- 18
Correct answer: 15
Scale factor = 25/10 = 2.5; corresponding leg = 6 × 2.5 = 15.
Bluebook SAT Test Right Triangles and Trigonometry 2
In right triangle ABC with the right angle at C, AB = 17 and BC = 8.
What is the value of tan(A)?