Standing at the edge of one bank of a river, a surveyor sees the top of a tree growing at the edge of the opposite bank at an angle of elevation of 60°. Walking 40 m straight back from the bank, she finds the angle of elevation is 30°. The width of the river is:

Question

Accepted Answer

20 m. Let the width be w and the tree height h. From the bank, h = w·tan60° = √3w. From 40 m further back, h = (w + 40)·tan30° = (w + 40)/√3. Equating: 3w = w + 40, so w = 20 m (and the tree is 20√3 ≈ 34.6 m tall — that is the height, not the width).

Standing at the edge of one bank of a river, a surveyor sees the top of a tree growing at the edge of the opposite bank at an angle of elevation of 60°. Walking 40 m straight back from the bank, she finds the angle of elevation is 30°. The width of the river is:

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