Bluebook SAT Test Right Triangles and Trigonometry 5 — Questions and Answers
Question 1: In right triangle XYZ with right angle at Z, XY = 25 and YZ = 7. What is cos(Y)?
- 7/25 (Correct answer)
- 24/25
- 7/24
- 24/7
Correct answer: 7/25
cos(Y) = adjacent/hypotenuse = YZ/XY = 7/25.
Question 2: A 30-60-90 triangle has the longer leg equal to 9√3. What is the length of the shorter leg?
- 9 (Correct answer)
- 18
- 9√2
- 3√3
Correct answer: 9
Longer leg = short leg × √3 = 9√3; short leg = 9.
Question 3: A wire is attached from the top of a 30-foot pole to a stake 16 feet from the base. How long is the wire?
- 34 (Correct answer)
- 32
- 46
- √866
Correct answer: 34
Wire² = 30² + 16² = 900 + 256 = 1156; wire = 34.
Question 4: In right triangle DEF with right angle at F, tan(D) = 3/4 and EF = 9. What is DE?
- 15 (Correct answer)
- 12
- 9
- 25
Correct answer: 15
tan(D) = EF/DF = 9/DF = 3/4; DF = 12; DE = √(9² + 12²) = √225 = 15.
Question 5: Two right triangles are similar. Their areas are 50 and 200 square units. What is the ratio of their corresponding sides?
- 1:2 (Correct answer)
- 1:4
- 1:√2
- 1:√3
Correct answer: 1:2
Area ratio = 50:200 = 1:4; side ratio = √(1/4) = 1:2.
Question 6: A right triangle has an acute angle of 60° and the side adjacent to that angle is 5. What is the hypotenuse?
- 10 (Correct answer)
- 5√3
- 5√2
- 10√3
Correct answer: 10
cos(60°) = 1/2 = adjacent/hypotenuse = 5/hyp; hyp = 10.
Question 7: In right triangle PQR with right angle at R, angle P = 45°. If PQ = 8√2, what is QR?
- 8 (Correct answer)
- 4√2
- 16
- 8√3
Correct answer: 8
45-45-90: legs = hyp/√2 = 8√2/√2 = 8.
Bluebook SAT Test Right Triangles and Trigonometry 5
In right triangle XYZ with right angle at Z, XY = 25 and YZ = 7.
What is cos(Y)?