Question

From a point on the ground, the angles of elevation of the top and bottom of
a transmission tower fixed at the top of a 20m high building are 600 and 45°
respectively. Find the height of the transmission tower.
A
=600
B
20m
009
45°
ace E Si QP​

Answer 1

Answer: 14.64m

Step-by-step explanation:

Refer to the attachment.

Let the height of the tower be x.

For triangle BDC

Tan theta= Perpendicular/Base

Where theta= 45°, perpendicular= 20m

Therefore- tan 45°= 20/Base

Therefore Base= 20m

Again for triangle ADC

tan theta = Perpendicular/Base

Where theta= 60°, perpendicular= 20+x and base = 20m

Therefore

Tan 60°= 20+x / 20

√3= 20+x / 20

√3×20= 20+x

34.64 - 20 =x

14.64m = x

Therefore the height of the tower is 14.64m.