Question

A tower stands vertically on the ground fom a point which is 12 meters away from the foot of the tower the angle of elevation of the top of the tower is 45 find the height of the tower

Answer 1

The height of the tower which is 12 m away from a point subtending 45 degrees to the top of the tower is 12 m.

Step-by-step explanation:

Referring to the figure attached below, let’s make some assumption

AB = h = height of the tower standing vertically on the ground

BC = 12 m = the distance of the foot of the tower from the point C

θ =  angle ACB = 45° = the angle of elevation of the tower  

Considering ∆ABC, applying the trigonometric ratios of a triangle, we get

tan θ = $\frac{Perpendicular}{Base}$

⇒ tan 45° = $\frac{AB}{BC}$

⇒  tan 45° = $\frac{h}{12}$

⇒ 1 = $\frac{h}{12}$

⇒ h = 12 m

Thus, the height of the tower is 12 m.

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