BMST Trigonometry and Right Triangle Relationships — Questions and Answers
Question 1: In a right triangle, if the opposite side is 3 and the hypotenuse is 5, what is sin(θ)?
- 3/5 (Correct answer)
- 4/5
- 3/4
- 5/3
Correct answer: 3/5
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?
- 8.66 m (Correct answer)
- 5.0 m
- 10.0 m
- 7.07 m
Correct answer: 8.66 m
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?
- 60° (Correct answer)
- 30°
- 45°
- 90°
Correct answer: 60°
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?
- 5/12 (Correct answer)
- 12/5
- 5/13
- 12/13
Correct answer: 5/12
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?
- 7.07 each (Correct answer)
- 5.0 each
- 8.66 and 5.0
- 6.0 and 8.0
Correct answer: 7.07 each
At 45°, the triangle is isosceles. Each leg = 10 × sin(45°) = 10 × (√2/2) ≈ 7.07.
Question 6: Which trigonometric ratio compares the adjacent side to the hypotenuse?
- Cosine (Correct answer)
- Sine
- Tangent
- Secant
Correct answer: Cosine
Cosine (CAH) = Adjacent / Hypotenuse. Sine = Opposite / Hypotenuse, and Tangent = Opposite / Adjacent.
BMST Trigonometry and Right Triangle Relationships
In a right triangle, if the opposite side is 3 and the hypotenuse is 5, what is sin(θ)?