ACT Math: Trigonometry 2 — Questions and Answers
Question 1: In a right triangle, the side opposite a 30° angle has length 5. What is the length of the hypotenuse?
- 10 (Correct answer)
- 5√3
- 5√2
- 2.5
Correct answer: 10
sin(30°) = opposite/hypotenuse = 1/2, so hypotenuse = 5 / (1/2) = 10.
Question 2: What is the exact value of cos(60°)?
- 1/2 (Correct answer)
- √3/2
- √2/2
- 1
Correct answer: 1/2
cos(60°) is a standard value equal to 1/2.
Question 3: If tan(θ) = 3/4 and θ is acute, what is sin(θ)?
- 3/5 (Correct answer)
- 4/5
- 5/3
- 4/3
Correct answer: 3/5
With opposite 3 and adjacent 4, the hypotenuse is 5, so sin(θ) = 3/5.
Question 4: Which identity is always true for any angle θ?
- sin²θ + cos²θ = 1 (Correct answer)
- sinθ + cosθ = 1
- tanθ = sinθ + cosθ
- sin²θ - cos²θ = 1
Correct answer: sin²θ + cos²θ = 1
The Pythagorean identity sin²θ + cos²θ = 1 holds for all angles.
Question 5: A ladder leans against a wall making a 70° angle with the ground. If the ladder is 12 ft long, how high up the wall does it reach (nearest tenth)?
- 11.3 ft (Correct answer)
- 4.1 ft
- 12.8 ft
- 6.0 ft
Correct answer: 11.3 ft
Height = 12 · sin(70°) ≈ 12 · 0.9397 ≈ 11.3 ft.
Question 6: What is the period of the function y = sin(x)?
- 2π (Correct answer)
- π
- π/2
- 4π
Correct answer: 2π
The sine function repeats every 2π radians.
Question 7: Convert 180° to radians.
- π (Correct answer)
- 2π
- π/2
- π/180
Correct answer: π
Since 180° equals half a circle, it equals π radians.
ACT Math: Trigonometry 2
In a right triangle, the side opposite a 30° angle has length 5.
What is the length of the hypotenuse?