From the top of a tower, the angle of depression of the top of a 10 m high building is 60°. If the distance between the tower and the building is 50√3 m, find the height of the tower.
160 m
The angle of depression is 60°. Therefore, we can use the tangent formula in right-angled triangles: \[ \tan(60^\circ) = \frac{\text{height of tower - height of building}}{\text{distance}} \] Substituting the known values: \[ \tan(60^\circ) = \frac{h - 10}{50\sqrt{3}} \] Using \(\tan(60^\circ) = \sqrt{3}\): \[ \sqrt{3} = \frac{h - 10}{50\sqrt{3}} \quad \Rightarrow \quad h - 10 = 150 \quad \Rightarrow \quad h = 160 \]
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