Discussion
The angles of depression and elevation of the top of a wall 11 m high from top and bottom of a tree are 60° and 30° respectively. What is the height of the tree?
Answer: D
The tree is taller than the wall, which is why the wall's top is seen below the horizontal from the tree's top.
From the tree's bottom, the wall top is at \( 30^{\circ} \):
\[ d = \frac{11}{\tan 30^{\circ}} = 11\sqrt{3} = 19.05 \text{ m} \]
From the tree's top it is \( H - 11 \) below, at \( 60^{\circ} \):
\[ H - 11 = d\tan 60^{\circ} = 11\sqrt{3} \times \sqrt{3} = 33 \]
\[ H = 33 + 11 = 44 \text{ m} \]
Because \( \tan 60^{\circ}\tan 30^{\circ} = 1 \), the tree works out at exactly four times the wall's height.
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