Bluebook SAT Test Right Triangles and Trigonometry 7 — Questions and Answers
Question 1: In right triangle ABC with right angle at C, AB = 20 and sin(A) = 3/5. What is BC?
- 12 (Correct answer)
- 15
- 16
- 9
Correct answer: 12
sin(A) = BC/AB = BC/20 = 3/5; BC = 12.
Question 2: A right isosceles triangle has a hypotenuse of 18. What is the area of the triangle?
- 81 (Correct answer)
- 72
- 81√2
- 162
Correct answer: 81
Legs = 18/√2 = 9√2; area = (1/2)(9√2)(9√2) = (1/2)(162) = 81.
Question 3: From the base of a hill, a climber walks 200 meters along a slope that makes a 30° angle with the horizontal. How high does the climber rise?
- 100 (Correct answer)
- 100√3
- 200√3
- 50√3
Correct answer: 100
Height = 200 sin(30°) = 200 × 1/2 = 100.
Question 4: In right triangle JKL with right angle at L, tan(K) = 2. If KL = 5, what is JL?
- 10 (Correct answer)
- 5/2
- √5
- √29
Correct answer: 10
tan(K) = JL/KL = JL/5 = 2; JL = 10.
Question 5: A right triangle has a hypotenuse of 10 and one acute angle of 37°. Which expression gives the leg opposite the 37° angle?
- 10 sin(37°) (Correct answer)
- 10 cos(37°)
- 10 tan(37°)
- 10/sin(37°)
Correct answer: 10 sin(37°)
sin(37°) = opposite/hypotenuse; opposite = 10 sin(37°).
Question 6: Two right triangles share the same hypotenuse of length 26. One has a leg of 10; the other has a leg of 24. Are both valid right triangles?
- Yes — 10-24-26 and both satisfy the Pythagorean theorem (Correct answer)
- No — only one satisfies the theorem
- Yes — but they are congruent
- No — neither satisfies the theorem
Correct answer: Yes — 10-24-26 and both satisfy the Pythagorean theorem
10² + 24² = 100 + 576 = 676 = 26²; both 10-24-26 (same triangle, just different legs named) satisfy the theorem.
Question 7: A 30-60-90 triangle has hypotenuse 22. What is the area of the triangle?
- (121√3)/2 (Correct answer)
- 121√3
- 44√3
- 121
Correct answer: (121√3)/2
Short leg = 11; long leg = 11√3; area = (1/2)(11)(11√3) = (121√3)/2.
Bluebook SAT Test Right Triangles and Trigonometry 7
In right triangle ABC with right angle at C, AB = 20 and sin(A) = 3/5.
What is BC?