A tower stands vertically on the ground. From a point on the grou… - Vidyadip

MCQ

A tower stands vertically on the ground. From a point on the ground which is $25 m$ away from the foot of the tower, the angle of elevation of the top of the tower is found to be $45^\circ$ . Then the height $($in meters$)$ of the tower is :

A
$25\sqrt{2}$
B
$25\sqrt{3}$
✓
$25$
D
$12.5$

✓

Answer

Correct option: C.

$25$

Let the height of the tower be $h.$
So $, AB = h$
Distance of the point from the foot of the tower $= 25m$
Hence $,CB = 25m$
Now,
$\tan\text{C}=\frac{\text{AB}}{\text{CB}}$
$\tan45^\circ=\frac{\text{AB}}{\text{CB}}$
$1=\frac{\text{h}}{25}$
$25=\text{h}$
Or $\text{h}=25$
Hence, height of the tower $= h = 25m.$

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