Bluebook SAT Test Right Triangles and Trigonometry 10 — Questions and Answers
Question 1: In right triangle XYZ with right angle at Z, XZ = 8 and XY = 17. What is cos(X)?
- 8/15
- 15/17
- 8/17 (Correct answer)
- 17/8
Correct answer: 8/17
XZ = 8 is adjacent to X and XY = 17 is the hypotenuse, so cos(X) = adjacent/hypotenuse = 8/17.
Question 2: A surveyor looks up at the top of a flagpole. The angle of elevation is 30° and the surveyor is 45 feet from the base. How tall is the flagpole?
- 45/√3
- 45√3
- 15√3 (Correct answer)
- 90
Correct answer: 15√3
tan(30°) = height/45, so height = 45·tan(30°) = 45·(1/√3) = 45/√3 = 45√3/3 = 15√3.
Question 3: A right triangle has a hypotenuse of 13 and one leg of 5. What is the sine of the larger acute angle?
- 5/13
- 12/13 (Correct answer)
- 5/12
- 13/12
Correct answer: 12/13
The other leg = √(169 − 25) = 12. The larger acute angle is opposite the longer leg (12), so sin = 12/13.
Question 4: In a 45-45-90 right triangle, if one leg has length 5, what is the length of the hypotenuse?
- 5
- 5√2 (Correct answer)
- 5√3
- 10
Correct answer: 5√2
In a 45-45-90 triangle, hypotenuse = leg × √2 = 5√2.
Question 5: Right triangle DEF has right angle at E. If tan(D) = 3 and EF = 6, what is DF?
- 2√10 (Correct answer)
- 6√10
- 3√10
- 18
Correct answer: 2√10
tan(D) = EF/DE = 6/DE = 3, so DE = 2. Then DF = √(DE² + EF²) = √(4 + 36) = √40 = 2√10.
Question 6: In right triangle ABC with right angle at C, angle A = 30° and AB = 12. What is the length of BC?
- 6 (Correct answer)
- 6√3
- 4√3
- 12√3
Correct answer: 6
sin(30°) = BC/AB = BC/12, so BC = 12 × sin(30°) = 12 × 0.5 = 6.
Question 7: In right triangle PQR with the right angle at R, PQ = 29 and QR = 21. What is sin(Q)?
- 21/29
- 20/29 (Correct answer)
- 21/20
- 20/21
Correct answer: 20/29
PR = √(PQ² − QR²) = √(841 − 441) = √400 = 20. sin(Q) = PR/PQ = 20/29.
Bluebook SAT Test Right Triangles and Trigonometry 10
In right triangle XYZ with right angle at Z, XZ = 8 and XY = 17.
What is cos(X)?