Question

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​

Answer 1

Let BC be the 20m high building.

D is the point on the ground from where the elevation is taken.

Height of transmission tower = AB = AC – BC

To Find: AB, Height of the tower

Let us consider in right ΔBCD,

tan 45° = $\frac{BC}{CD}$

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

CD = 20

Again,

In right ΔACD,

tan 60° = $\frac{AC}{CD}$

√3 = $\frac{AC}{20}$

AC = 20√3

Now, AB = AC – BC = (20√3 – 20) = 20(√3 – 1)

Hence, the height of the transmission tower is 20(√3 – 1) m.

Answer 2

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