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JAMB 1988 · UME · Q39

From a point 14314\sqrt3 m away from a tree, a man finds that the angle of elevation of the top of the tree is 30∘30^\circ. If he measures this angle from a point 2 m above the ground, how high is the tree?

Worked solution (try it first)
  1. The angle is measured at his eye, so first find the height of the top above eye level: 143×tan⁡30∘14\sqrt3 \times \tan30^\circ.
  2. Since tan⁡30∘=13\tan30^\circ = \frac{1}{\sqrt3}, that is 14 m.
  3. Add the 2 m from the ground to his eye: the tree is 14+2=1614 + 2 = 16 m, option D.

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