Bluebook SAT Test Geometry and Trigonometry 2 — Questions and Answers
Question 1: An isosceles triangle has two equal sides of length 9 and a base of 6. What is its perimeter?
- 15
- 18
- 24 (Correct answer)
- 30
Correct answer: 24
Perimeter = 9 + 9 + 6 = 24.
An isosceles triangle has two sides of equal length. Here the two equal sides are 9 each, and the base is 6. Perimeter = 9 + 9 + 6 = 24 units.
Question 2: In a right triangle, tan(30°) = ?
- √3
- 1/√3 (Correct answer)
- √3/2
- 1/2
Correct answer: 1/√3
tan(30°) = sin(30°)/cos(30°) = (1/2)/(√3/2) = 1/√3.
In a 30-60-90 triangle, the sides are in ratio 1 : √3 : 2. For the 30° angle: opposite = 1, adjacent = √3. So tan(30°) = 1/√3 = √3/3. This can also be found using sin(30°)/cos(30°) = (1/2)/(√3/2) = 1/√3.
Question 3: A right triangle has a hypotenuse of 13 and one leg of 5. What is the other leg?
- 8
- 10
- 11
- 12 (Correct answer)
Correct answer: 12
a² + 5² = 13² → a² = 169 − 25 = 144 → a = 12.
Using the Pythagorean theorem: a² + b² = c². Here a² + 5² = 13², so a² + 25 = 169, giving a² = 144 and a = 12. This is the classic 5-12-13 Pythagorean triple.
Question 4: What is the area of a triangle with base 10 and height 8?
- 20
- 40 (Correct answer)
- 80
- 18
Correct answer: 40
Area = (1/2) × base × height = (1/2)(10)(8) = 40.
The formula for the area of a triangle is A = (1/2)bh. With base = 10 and height = 8: A = (1/2)(10)(8) = (1/2)(80) = 40 square units.
Question 5: Two supplementary angles are in a ratio of 2:3. What is the measure of the larger angle?
- 72°
- 90°
- 108° (Correct answer)
- 120°
Correct answer: 108°
Supplementary angles sum to 180°. Larger angle = (3/5) × 180° = 108°.
Supplementary angles sum to 180°. If the ratio is 2:3, the angles are 2k and 3k where 2k + 3k = 180°, so 5k = 180° and k = 36°. The larger angle is 3k = 108°.
Question 6: A cylinder has radius 3 and height 10. What is its volume? (Use π ≈ 3.14)
- 94.2
- 188.4
- 282.6 (Correct answer)
- 565.2
Correct answer: 282.6
V = πr²h = 3.14 × 9 × 10 = 282.6.
The volume of a cylinder is V = πr²h. With r = 3 and h = 10: V = π × 3² × 10 = π × 9 × 10 = 90π ≈ 3.14 × 90 = 282.6 cubic units.
Question 7: If cos(θ) = 5/13 in a right triangle, what is sin(θ)?
- 5/12
- 12/13 (Correct answer)
- 13/5
- 8/13
Correct answer: 12/13
Using sin²θ + cos²θ = 1: sin²θ = 1 − 25/169 = 144/169, so sinθ = 12/13.
In a right triangle with cos(θ) = 5/13, the adjacent side is 5 and hypotenuse is 13. The opposite side = √(13² − 5²) = √(169 − 25) = √144 = 12. So sin(θ) = opposite/hypotenuse = 12/13.
Question 8: A square has a diagonal of 8√2. What is the side length of the square?
- 4
- 8 (Correct answer)
- 16
- 4√2
Correct answer: 8
Diagonal of square = s√2. So s√2 = 8√2 → s = 8.
For a square with side length s, the diagonal d = s√2 (from the Pythagorean theorem: d² = s² + s² = 2s²). Given d = 8√2: s√2 = 8√2, so s = 8.
Bluebook SAT Test Geometry and Trigonometry 2
An isosceles triangle has two equal sides of length 9 and a base of 6.
What is its perimeter?