BMST Trigonometry and Right Triangle Relationships

Question 1

In a right triangle, if the opposite side is 3 and the hypotenuse is 5, what is sin(θ)?

Accepted Answer

3/5

Answer

Sine is defined as opposite/hypotenuse. With opposite = 3 and hypotenuse = 5, sin(θ) = 3/5 = 0.6.

Question 2

A ladder leans against a wall making a 60° angle with the ground. If the ladder is 10 meters long, how high up the wall does it reach?

Accepted Answer

8.66 m

Answer

The height = 10 × sin(60°) = 10 × (√3/2) ≈ 8.66 m. The side opposite to the 60° angle is found using sine.

Question 3

If cos(θ) = 0.5, what is the angle θ?

Accepted Answer

60°

Answer

cos(60°) = 0.5 is a standard reference angle. Memorizing the cosine of 30°, 45°, and 60° is essential for BMST math.

Question 4

In a right triangle with legs of length 5 and 12, what is the tangent of the angle opposite the side of length 5?

Accepted Answer

5/12

Answer

Tangent = opposite/adjacent. The side opposite the angle is 5, and the adjacent side is 12, so tan(θ) = 5/12.

Question 5

A right triangle has an angle of 45°. If the hypotenuse is 10, what are the lengths of each leg?

Accepted Answer

7.07 each

Answer

At 45°, the triangle is isosceles. Each leg = 10 × sin(45°) = 10 × (√2/2) ≈ 7.07.

BMST - Basic Math and Science Test Practice Test