Geometry and TrigonometryHardHeight of a pole from an angle of elevation
Geometry and Trigonometry practice question
From a point 12 metres from the base of a vertical pole, the angle of elevation to the top of the pole is 30°. What is the height of the pole, in metres?
- A. 4√3Correct
- B. 12√3
- C. 6
- D. 24
Answer: A. 4√3
height = 12 tan 30° = 12/√3 = 4√3.
Why the other answers are wrong
- B. 12√3
- 12√3 uses tan 60° instead of tan 30°.
- C. 6
- 6 uses sin 30° as though 12 were the hypotenuse.
- D. 24
- 24 treats 12 as the side opposite 30° in a 30-60-90 triangle.
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