Class 10

Math

All topics

Some Applications of Trigonometry

A tower stands vertically on the ground. From a point on the ground which is $30m$ away from the foot of a tower, the angle of elevation of the top of the tower is found to be $45_{o}$. Find the height of tower.

- $15$
- $40$
- $30$
- $20$

REF.Image.

$30m$ away / $45_{∘}$ inclination.

Let the height of tower be h m

so $AB=hm$

Distance of the point from

foot of tower = $30m$

$CB=30m$

Angle of elevation $=45_{∘}$

$∠ACB=45_{∘}$

Since tower is vertical to ground

$∠ABC=90_{∘}$

Now $tanC=sideadjacenttoangleCsideopptoangleC $

$tanC=CBAB $

$tan45=CBAB $

$1=30H $

$H=30$

Hence height of tower = $30m$

Answer = option $C=30m$