From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find 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

BC denotes the building, AB the transmission tower, and D a point on the ground
Let BC represent the building, AB the transmission tower, and D a point on the ground from which elevation angles are measured.

In triangle BCD,

$\frac{BC}{CD} = tan45° $

$\frac{20}{ CD} =1$

$CD = 20m$

In triangle ACD,

$\frac{AC}{ CD }= tan 60°$

$\frac{AB + BC}{ CD} = \sqrt3$

$\frac{AB + 20}{ 20} = \sqrt3$

$AB = (20\sqrt3 -20)\, m$

$AB = 20(\sqrt3 -1)\,m$

Consequently, the height of the transmission tower is $20(\sqrt3 -1)\,m$.

From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.

Solution and Explanation

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