DSAT DSAT Geometry and Trigonometry 2 — Questions and Answers
Question 1: In a 30-60-90 triangle, the side opposite the 30° angle is 6. What is the length of the hypotenuse?
- 6√3
- 12 (Correct answer)
- 6√2
- 18
Correct answer: 12
In a 30-60-90 triangle, the hypotenuse is twice the shortest side: 2 × 6 = 12.
Question 2: What is the slope of a line passing through the points (2, 3) and (6, 11)?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
Slope = (y₂ − y₁) / (x₂ − x₁) = (11 − 3) / (6 − 2) = 8 / 4 = 2.
Question 3: A sector of a circle has a central angle of 90° and a radius of 8. What is the area of the sector?
- 8π
- 16π (Correct answer)
- 32π
- 64π
Correct answer: 16π
Area of a sector = (θ/360) × πr² = (90/360) × π(64) = (1/4) × 64π = 16π.
Question 4: The exterior angle of a triangle measures 120°. If one of the non-adjacent interior angles is 45°, what is the other non-adjacent interior angle?
- 60°
- 75° (Correct answer)
- 90°
- 80°
Correct answer: 75°
An exterior angle equals the sum of the two non-adjacent interior angles: 120° = 45° + x, so x = 75°.
Question 5: If sin(θ) = 3/5 in a right triangle, what is cos(θ)?
- 4/5 (Correct answer)
- 3/4
- 5/3
- 5/4
Correct answer: 4/5
Using a 3-4-5 right triangle where sin(θ) = 3/5, the adjacent side is 4, so cos(θ) = 4/5.
Question 6: What is the area of a trapezoid with parallel sides of length 8 and 12, and a height of 5?
- 40
- 50 (Correct answer)
- 60
- 100
Correct answer: 50
Area of a trapezoid = ½ × (b₁ + b₂) × h = ½ × (8 + 12) × 5 = ½ × 20 × 5 = 50.
DSAT DSAT Geometry and Trigonometry 2
In a 30-60-90 triangle, the side opposite the 30° angle is 6.
What is the length of the hypotenuse?