SATs Geometry & Trigonometry 2 — Questions and Answers
Question 1: In a 30-60-90 triangle, the shortest leg measures 6. What is the length of the hypotenuse?
- 6√3
- 12 (Correct answer)
- 6√2
- 9
Correct answer: 12
In a 30-60-90 triangle the hypotenuse is twice the shortest leg: 2 × 6 = 12.
Question 2: What is the slope of the line passing through points (2, 4) and (6, 12)?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
Slope = (12 − 4) / (6 − 2) = 8 / 4 = 2.
Question 3: If tan(θ) = 1 and 0° < θ < 90°, what is θ?
- 30°
- 45° (Correct answer)
- 60°
- 90°
Correct answer: 45°
tan(45°) = 1 because sin(45°) = cos(45°) = √2/2.
Question 4: What is the perimeter of an equilateral triangle with side length 9?
- 18
- 27 (Correct answer)
- 36
- 81
Correct answer: 27
Perimeter = 3s = 3(9) = 27.
Question 5: A sector of a circle has a central angle of 90° and a radius of 8. What is its arc length?
- 2π
- 4π (Correct answer)
- 8π
- 16π
Correct answer: 4π
Arc length = (90/360) × 2π(8) = (1/4)(16π) = 4π.
Question 6: A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?
- 11
- 13 (Correct answer)
- 15
- 17
Correct answer: 13
c² = 5² + 12² = 25 + 144 = 169, so c = 13 (a standard Pythagorean triple).
Question 7: What is the area of a square whose diagonal measures 10?
- 25
- 50 (Correct answer)
- 100
- 50√2
Correct answer: 50
For a square with diagonal d, the side s = d/√2 and area = s² = d²/2 = 100/2 = 50.
SATs Geometry & Trigonometry 2
In a 30-60-90 triangle, the shortest leg measures 6.
What is the length of the hypotenuse?