Question

A pole 8m high is fixed on the top of the tower the angle of elevation of top of as the pole as observed from a point A on the ground is alpha such that sin alpha = 4/5 and the angle of depression of point A from the top of tower is 45°what is the height of the tower​

Answer 1

Answer:

A pole 8m high is fixed on the top of the tower the angle of elevation of top of as the pole as observed from a point A on the ground is alpha such that sin alpha = 4/5 and the angle of depression of point A from the top of tower is 45°what is the height of the tower

Answer 2

The height of tower is 24 meter.

Step-by-step explanation:

Given:

8 meter high a pole is fixed on the top of the tower.

the angle of elevation on top of the pole as observed from a point A on the ground is an alpha and sin $\alpha$  = 4/5.

The angle of depression of point A from the top of the tower is $45\textdegree$.

To Find:

The height of tower.

Formula Used:

$tan\theta = \frac{perpendicular}{base}$  

Identity  $sin^{2}x+cos^{2} x=1$

Solution:

Let the height of the tower is P.

Let the distance between the tower and point A is Q.

As given -the height of the pole is 8m.

 As given - the Angle of depression from the top of tower to point A is $45\textdegree$.

Then,  $tan 45\textdegree = \frac{P}{Q}$

                  $1=\frac{P}{Q}$

                  $Q=P$   -------------- equation no.01

As given - the angle of elevation on top of the pole as observed from a point A on the ground is an alpha and sin $\alpha$ = 4/5.

$sin\alpha =\frac{4}{5}$

Using identity $sin^{2}\alpha +cos^{2} \alpha =1$

$cos^{2} \alpha =1-sin^{2}\alpha$

$cos\alpha =\sqrt{ 1-sin^{2}\alpha }$

$cos\alpha =\sqrt{ 1-(\frac{4}{5} )^{2} }$    

$cos\alpha =\sqrt{ 1-(\frac{16}{25} ) }$

$cos\alpha =\sqrt{ (\frac{25-16}{25} ) }$  

$cos\alpha =\sqrt{ (\frac{9}{25} ) } =\frac{3}{5}$

$tan\alpha =\frac{sin\alpha }{cos\alpha } = \frac{\frac{4}{5} }{\frac{3}{5} }$

$tan\alpha =\frac{4}{3}$

Then,  $\frac{4}{3} =\frac{8+P}{Q}$

Putting the value of Q from equation no.01.

$\frac{4}{3} =\frac{8+P}{P}$

$4P= 24+ 3P$

$P=24$

Thus, the height of tower is 24 meter.