Question

from the top of a tower of height 50m the angles of depression of the top and bottom of a polar 30 degree and 45 degree respectively find the height of the pole

Answer 1

See the pic to get your answer .

Answer 2

Answer:

21.133 m

Step-by-step explanation:

Refer the attached figure

Height of tower = AC = 50 m

Height of pole = ED =CB = 50-x

In ΔABE

$tan \theta = \frac{Perpendicular}{Base}$

$tan 30= \frac{AB}{BE}$

$tan 30= \frac{x}{BE}$

$\frac{1}{\sqrt{3}= \frac{x}{BE}$

$BE= \sqrt{3}x$ ---A

In ΔACD

$tan \theta = \frac{Perpendicular}{Base}$

$tan 45= \frac{AC}{CD}$

$1= \frac{50}{CD}$

Since CD = BE

So, $1= \frac{50}{BE}$

BE = 50

Substitute the value in A

$50= \sqrt{3}x$

$\frac{50}{\sqrt{3}}= x$

$28.867= x$

So,  ED =CB = 50-x = 50 - 28.867 = 21.133 m

Hence The height of the pole is 21.133 m