Bluebook SAT Test Right Triangles and Trigonometry 1 — Questions and Answers
Question 1: A right triangle has legs of length 9 and 12. What is the length of the hypotenuse?
- 15 (Correct answer)
- 18
- 14
- 21
Correct answer: 15
By the Pythagorean theorem: c² = 9² + 12² = 81 + 144 = 225, so c = 15.
Question 2: In right triangle ABC with the right angle at C, sin(A) = 3/5. What is cos(A)?
- 4/5 (Correct answer)
- 3/4
- 5/3
- 5/4
Correct answer: 4/5
Since sin²(A) + cos²(A) = 1: cos(A) = √(1 − 9/25) = √(16/25) = 4/5.
Question 3: A 30-60-90 triangle has the shortest leg equal to 7. What is the length of the hypotenuse?
- 14 (Correct answer)
- 7√2
- 7√3
- 21
Correct answer: 14
In a 30-60-90 triangle the hypotenuse is twice the shortest leg: 2 × 7 = 14.
Question 4: In right triangle PQR with the right angle at R, tan(P) = 5/12. If QR = 5, what is PR?
- 12 (Correct answer)
- 13
- 5
- 60
Correct answer: 12
tan(P) = opposite/adjacent = QR/PR = 5/PR; solving, PR = 5 × 12/5 = 12.
Question 5: A ladder leans against a wall, making a 60° angle with the ground. If the ladder is 20 feet long, how high on the wall does it reach?
- 10√3 (Correct answer)
- 10
- 20√3
- 10√2
Correct answer: 10√3
Height = 20 sin(60°) = 20 × (√3/2) = 10√3.
Question 6: A 45-45-90 triangle has a hypotenuse of 10√2. What is the length of each leg?
- 10 (Correct answer)
- 5√2
- 10√2
- 5
Correct answer: 10
In a 45-45-90 triangle, leg = hypotenuse/√2 = 10√2/√2 = 10.
Question 7: In right triangle DEF with the right angle at F, DE = 13 and EF = 5. What is sin(E)?
- 12/13 (Correct answer)
- 5/13
- 12/5
- 5/12
Correct answer: 12/13
DF = √(13² − 5²) = √(169 − 25) = √144 = 12; sin(E) = opposite/hypotenuse = DF/DE = 12/13.
Bluebook SAT Test Right Triangles and Trigonometry 1
A right triangle has legs of length 9 and 12.
What is the length of the hypotenuse?