From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

Question

A ladder 14 m long just reaches the top of a vertical wall. If the ladder makes an angle of $60^\circ$ with the wall, then the height of the wall is:

Answer 1

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60°
Let AB represent the building and CD represent the cable tower.

In right triangle ABD,

$\frac{AB}{ BD} = \tan 45^{\degree}$

$\frac{7}{ BD} = 1$

$BD = 7\,m$

In right triangle ACE,

$AC = BD = 7m$

$\frac{CE}{ AE} = \tan 60^{\degree}$

$\frac{CE}{7} = \sqrt3$

$CE = 7\sqrt3$

$CD = CE + ED = (7\sqrt3 +7)m$

$CD= 7(\sqrt3 + 1)\,m$

Consequently, the height of the cable tower is $7(\sqrt3+1) \,m$.

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

Solution and Explanation

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