Geometry and TrigonometryMediumHeight of a tree from an angle of elevation
Geometry and Trigonometry practice question
From a point 10 metres from the base of a tree, on level ground, the angle of elevation to the top of the tree is 60°. What is the height of the tree, in metres? Give your answer to the nearest tenth.
Answer: 17.3
tan 60° = height/10, so height = 10 tan 60° = 10√3 ≈ 17.3 metres.
Common wrong answers
- If you answered 20
- 20 is 10 ÷ cos 60°, the distance to the TOP of the tree (the hypotenuse).
- If you answered 5.8
- 5.8 is 10 ÷ √3 (10 tan 30°), using the wrong angle.
- If you answered 8.7
- 8.7 is 10 sin 60°, which would need 10 to be the hypotenuse.
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