Question

the angles of depression of the top and bottom of a tower as seen from the top of a 60 root 3 high cliff are 45 degree and 60 degree respectively find the height of the tower and the distance between the foot of the cliff and the foot of the tower

Answer 1

please mark it as the brainliest answer

Answer 2

Given :

The angles of depression of the top and bottom of a tower as seen from the top of a 60 root 3 high cliff are 45 degree and 60 degree respectively

To Find :

find the height of the tower and the distance between the foot of the cliff and the foot of the tower

Solution:

Refer the attached figure

Height of cliff AC =$60 \sqrt{3}$

We are given that The angles of depression of the top and bottom of a tower as seen from the top of a cliff are 45 degree and 60 degree

DC is the distance between the foot of the cliff and the foot of the tower

So,$\angle AEB = 45^{\circ}\\\angle ADC = 60^{\circ}$

In ΔADC

$Tan\theta = \frac{Perpendicular}{Base}\\Tan 60^{\circ}=\frac{AC}{DC}\\\sqrt{3}=\frac{60\sqrt{3}}{DC}\\DC = \frac{60\sqrt{3}}{\sqrt{3}}\\DC = 60\\DC=EB=60$

Height of tower = DE

In ΔABE

$Tan \theta = \frac{AB}{BE}\\Tan 45^{\circ}=\frac{AB}{60}\\1=\frac{AB}{60}\\AB = 60\\BC = AC- AB = 60 \sqrt{3}-60=43.923\\BC=DE = 43.923$

So, the height of the tower is 43.923

Hence  the height of the tower is 43.923  and the distance between the foot of the cliff and the foot of the tower is 60