Geometry

Trigonometry

Medium

The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower when seen from the foot of the building is 60°. If the tower is 60 m high, then the height of the building is:

35 m

20 m

25 m

30 m

✅ Correct Option: 2

Let the height of the building be $h$ and the distance between the tower and building be $d$ .

Tower height = 60 m

Angle from building's foot to tower's top = 60°

Angle from tower's foot to building's top = 30°

From the foot of the building, looking at the top of the tower:

$\tan(60°) = \frac{60}{d}$

$\sqrt{3} = \frac{60}{d}$

$d = \frac{60}{\sqrt{3}}$

$d = 20\sqrt{3}$ m

From the foot of the tower, looking at the top of the building:

$\tan(30°) = \frac{h}{d}$

$\frac{1}{\sqrt{3}} = \frac{h}{d}$

Substituting $d = 20\sqrt{3}$ :

$\frac{1}{\sqrt{3}} = \frac{h}{20\sqrt{3}}$

$h = \frac{20\sqrt{3}}{\sqrt{3}}$

$h = 20$ m

The height of the building is 20 m.

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