Question

the angle of elevation of the top of a tower at a pt on the horizontal line through the foot of the tower is 45 degree after walking a distance of 80m towards the foot of the tower along the same horizontal line the angle of elevation of the top of the tower changes to 60 degree find the height of the tower

Answer 1

HOPE IT'S HELPFUL ! ❤️

HAVE A NICE DAY !!

Answer 2

The answer is 189 m

The height of the tower is 189 m

Given:

The angle of elevation at first point is 45°

The angle of elevation at second point is 60°

Distance from the foot of the observer to the tower is

80m

To Find:

Height of the tower

Solution:

In ∆ ADC

tan 45° = h/ 80+y

h = 80+ y

In ∆ ADC

tan 60° = h/y

√3 = h/y

√3 = 80+ y/ y

√3 y = 80+ y

80 = √3 y -y

80 = y (√3-1)

y = 80/ √3 -1. × √3+1/√3-1

= 80(√3 +1)/3-1

= 40(√3+1)

H = 80+ 40(√3+1)

= 40 ( 2+√3+1)

= 120 + 40√3

= 120 + 40( 1.732)

= 189

The height of the tower is 189 m