Question

A building and a tower are on the same level ground. The angle of elevation of the top of the building from the foot of the tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the height of the tower is 50 m, then find the height of the building.

Answer 1

Answer:

Height of building is 16.66 m.

Step-by-step explanation:

In Figure let the AB = Building of height h and CD = Tower of height 50 m.

and BC is the distance between the foots of building and tower.

In $\Delta ABC$

$\tan 30^\circ = \cfrac{AB}{BC}$

$\Rightarrow \cfrac{1}{\sqrt{3}} = \cfrac{h}{BC}$

$\Rightarrow BC=h\sqrt{3}$     ...(1)

Now, in $\Delta DCB$

$\tan 60^\circ = \cfrac{CD}{BC}$

$\Rightarrow \sqrt{3} = \cfrac{50}{BC}$

$\Rightarrow BC=\cfrac{50}{\sqrt3}$         ...(2)

From Eqns. (1) and (2), we get

$h\sqrt{3} = \cfrac{50}{\sqrt{3}}$

$\Rightarrow h = \cfrac{50}{3} = 16.66 \text{ m}$

Please mark my answer as BRAINLIEST.