Chapter 12: Applications of Trigonometry — Online MCQ Test
MATHS · CLASS 10th · Telangana State Board
Practice Chapter 12: Applications of Trigonometry with a free chapter-wise online MCQ test.
This chapter covers: Applying trigonometric concepts to practical situations.
AI-generated questions from basic to board-exam level, with instant results and explanations.
Chapter 12: Applications of Trigonometry — Important Questions & Answers
The angle of elevation is defined as the angle between the horizontal line and the line of sight when looking at an object that is:
- A. Below the observer's eye level
- B. Above the observer's eye level
- C. At the same level as the observer
- D. Behind the observer
Answer: B. Above the observer's eye level
Angle of elevation is the angle formed above the horizontal when looking upward at an object.
Angle of elevation is the angle formed above the horizontal when looking upward at an object.
If a person standing 50 m away from a building looks up at the top with an angle of elevation of 60°, what is the height of the building? (Use √3 ≈ 1.732)
- A. 50√3 m
- B. 50/√3 m
- C. 100 m
- D. 25√3 m
Answer: A. 50√3 m
Using tan(60°) = height/distance, we get height = 50 × tan(60°) = 50√3 m.
Using tan(60°) = height/distance, we get height = 50 × tan(60°) = 50√3 m.
A ladder leaning against a wall makes an angle of 60° with the ground. If the ladder is 10 m long, how high does it reach on the wall?
- A. 5 m
- B. 5√3 m
- C. 10√3 m
- D. 10 m
Answer: B. 5√3 m
Height = ladder length × sin(60°) = 10 × (√3/2) = 5√3 m.
Height = ladder length × sin(60°) = 10 × (√3/2) = 5√3 m.
A person observes the angle of elevation to the top of a mountain from point A as 30°. After moving 100 m closer to the mountain (point B), the angle of elevation becomes 60°. Which of the following is NOT required to find the height of the mountain?
- A. The distance moved (100 m)
- B. The initial angle (30°)
- C. The final angle (60°)
- D. The person's height
Answer: D. The person's height
The person's height is not needed in this problem as we're dealing with angles of elevation from a reference point, not absolute heights from ground level.
The person's height is not needed in this problem as we're dealing with angles of elevation from a reference point, not absolute heights from ground level.
An observer at the top of a 50 m tall lighthouse observes two ships. Ship A is at an angle of depression of 30°, and Ship B is at an angle of depression of 45°. Which statement is true?
- A. Ship A is closer to the lighthouse
- B. Ship B is closer to the lighthouse
- C. Both ships are equidistant
- D. Ship A is 50 m away
Answer: B. Ship B is closer to the lighthouse
Distance = height/tan(angle). Ship A: 50/tan(30°) = 50√3 ≈ 86.6 m. Ship B: 50/tan(45°) = 50 m. Ship B is closer.
Distance = height/tan(angle). Ship A: 50/tan(30°) = 50√3 ≈ 86.6 m. Ship B: 50/tan(45°) = 50 m. Ship B is closer.