2017 · Q69
From the top of a building 90 m high, the angles of depression of the top and the bottom of a tree are 30° and 45° respectively. What is the height of the tree ?
Elementary MathematicsTrigonometry
- A30√(3) m
- B90 - 30√(3) m
- C90 + 30√(3) m
- D60 + 30√(3) m
Explanation
The tree's base is depressed 45° from 90 m up, so it is 90 m away horizontally. The tree top is depressed 30°, i.e. 90·tan30° = 30√3 m below the observer. Tree height = 90 − 30√3 m: option B.