Geometry and TrigonometryVery hardHeight of a kite from an angle of elevation
Geometry and Trigonometry practice question
A kite string is 20 metres long and makes a 30° angle with the level ground. Assuming the string is straight, how high above the ground is the kite?
- A. 10 mCorrect
- B. 10√3 m
- C. 20√3 m
- D. 10√2 m
Answer: A. 10 m
The height is the side opposite the 30° angle, and the string is the hypotenuse: height = 20 × sin 30° = 20 × 1/2 = 10 m.
Why the other answers are wrong
- B. 10√3 m
- 10√3 is 20 × cos 30°, the HORIZONTAL distance from the flyer to the point below the kite.
- C. 20√3 m
- 20√3 is more than the string's length, which is impossible for a height.
- D. 10√2 m
- 10√2 would be the height at a 45° angle.
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