Question

from a top of a building 15m high the angle of elevation of the top of a tower is found to be 30° from the bottom of same building the angle of elevation of the top of tower is found to be 45° determine the height of tower and distance between them

Answer 1

Answer:

35.49 m

Step-by-step explanation:

Refer the attached figure

Height of the building = AB = 15 m

AB = CD = 15 m

AD=BC

Let DE be x

Height of tower = CE = CD+DE=15+x

The angle of elevation of the top of a tower is found to be 30° i.e.∠EAD = 30°

From the bottom of same building the angle of elevation of the top of tower is found to be 45° i.e. ∠EBC = 45°

In ΔEAD

$Tan \tehta = \frac{Perpendicular}{Base}$

$Tan 30^{\circ} = \frac{ED}{AD}$

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

$AD= \frac{x}{\frac{1}{\sqrt{3}}}$  ---1

In ΔEBC

$Tan \tehta = \frac{Perpendicular}{Base}$

$Tan 45^{\circ} = \frac{EC}{BC}$

$1= \frac{15+x}{BC}$

$BC = 15+x$ ---2

Equate 1 and 2

$15+x= \frac{x}{\frac{1}{\sqrt{3}}}$

$x=20.490$

Height of tower = 15+x=15+20.490=35.49 m

So, BC = 15+x=35.49 m

Hence the height of tower and distance between them is 35.49 m