A vertical pole and a vertical tower are on the same level ground. From the top of the pole, the angle of elevation of the top of the tower is $60^\circ$ and the angle of depression of the foot of the tower is $30^\circ$. The height of the tower if the height of the pole is 20 m, is ______.

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A vertical pole and a vertical tower are on the same level ground. From the top of the pole, the angle of elevation of the top of the tower is $60^\circ$ and the angle of depression of the foot of the tower is $30^\circ$. The height of the tower if the height of the pole is 20 m, is 80 m. Explanation: Let pole height = 20 m and tower height = H. Let horizontal distance between them = x. From the top of the pole: Angle of depression to the foot of the tower $30^\circ$ $\Rightarrow$ tan 30^circ = 20/x = 1/sqrt(3) $\Rightarrow$ x = 20sqrt(3) Angle of elevation to the top of the tower $60^\circ$ $\Rightarrow$ tan 60^circ = (H - 20)/x = sqrt(3) $\Rightarrow$ H - 20 = xsqrt(3) = (20sqrt(3))(sqrt(3)) = 60 So, H = 20 + 60 = 80 m

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