The angle of elevation of the top of a hill at the foot of a tower is $60^\circ$ and the angle of depression from the top of the tower of the foot of the hill is $30^\circ$. If the tower is 50 m high, the height of the hill is ______.

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The angle of elevation of the top of a hill at the foot of a tower is $60^\circ$ and the angle of depression from the top of the tower of the foot of the hill is $30^\circ$. If the tower is 50 m high, the height of the hill is 150 m. Explanation: Let BD = x be the horizontal distance between the tower and the hill. From the top of the tower height 50 m the angle of depression to the foot of the hill is $30^\circ$. So, tan 30^circ = 50/x $\Rightarrow$ x = 50sqrt(3) At the foot of the tower the angle of elevation to the top of the hill is $60^\circ$. So, tan 60^circ = h/x $\Rightarrow$ h = sqrt(3) xx x = sqrt(3) xx (50sqrt(3)) = 150 m

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