Bluebook SAT Test Right Triangles and Trigonometry 4 — Questions and Answers
Question 1: In right triangle ABC with the right angle at C, tan(A) = 7/24. What is the length of the hypotenuse if AC = 24?
- 25 (Correct answer)
- 26
- 28
- 7
Correct answer: 25
tan(A) = BC/AC = 7/24, so BC = 7; hyp = √(7² + 24²) = √(49 + 576) = √625 = 25.
Question 2: A 45-45-90 triangle has a perimeter of 20 + 10√2. What is the length of the hypotenuse?
- 10√2 (Correct answer)
- 10
- 20
- 5√2
Correct answer: 10√2
Let each leg = a; perimeter = 2a + a√2 = a(2 + √2) = 20 + 10√2 = 10(2 + √2); so a = 10 and hyp = 10√2.
Question 3: In right triangle RST with right angle at T, RS = 15 and RT = 9. What is sin(R)?
- 4/5 (Correct answer)
- 3/5
- 4/3
- 5/4
Correct answer: 4/5
ST = √(15² − 9²) = √(225 − 81) = √144 = 12; sin(R) = ST/RS = 12/15 = 4/5.
Question 4: From a point on level ground, the angle of elevation to the top of a 60-meter building is 45°. How far is the point from the base of the building?
- 60 (Correct answer)
- 60√2
- 30√2
- 30
Correct answer: 60
tan(45°) = 1 = 60/d; d = 60.
Question 5: A right triangle has a hypotenuse of 2 and one leg of √3. What is the measure of the smallest angle?
- 30° (Correct answer)
- 45°
- 60°
- 90°
Correct answer: 30°
Other leg = √(4 − 3) = 1; the triangle has sides 1, √3, 2 — a 30-60-90 triangle; smallest angle = 30°.
Question 6: In similar right triangles, the ratio of the shorter legs is 3:7. If the area of the smaller triangle is 27 square units, what is the area of the larger triangle?
- 147 (Correct answer)
- 63
- 189
- 441
Correct answer: 147
Area scales as the square of the linear ratio: (7/3)² × 27 = 49/9 × 27 = 147.
Question 7: In right triangle ABC with right angle at C, cos(A) = 12/13. What is tan(A)?
- 5/12 (Correct answer)
- 5/13
- 12/5
- 13/12
Correct answer: 5/12
sin(A) = √(1 − 144/169) = 5/13; tan(A) = sin/cos = (5/13)/(12/13) = 5/12.
Bluebook SAT Test Right Triangles and Trigonometry 4
In right triangle ABC with the right angle at C, tan(A) = 7/24.
What is the length of the hypotenuse if AC = 24?