ACT Math: Trigonometry 2

Question 1

In a right triangle, the side opposite a 30° angle has length 5. What is the length of the hypotenuse?

Accepted Answer

10

Answer

sin(30°) = opposite/hypotenuse = 1/2, so hypotenuse = 5 / (1/2) = 10.

Question 2

What is the exact value of cos(60°)?

Accepted Answer

1/2

Answer

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)?

Accepted Answer

3/5

Answer

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?

Accepted Answer

sin²θ + cos²θ = 1

Answer

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)?

Accepted Answer

11.3 ft

Answer

Height = 12 · sin(70°) ≈ 12 · 0.9397 ≈ 11.3 ft.

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