A tower stand vertically on the ground.

Question:

A tower stand vertically on the ground. From a point on the ground 20 m away from the foot of the tower, the angle of elevation of the top of the tower is 60°. What is the height of the tower?

Solution:

Let  be the tower of height m and C be the point on the ground, makes an angle of elevation with the top of tower.

In a triangle, given that BC = 20 m and 

Now we have to find height of tower, so we use trigonometrical ratios.

In the triangle,

$\Rightarrow \tan C=\frac{A B}{B C}$

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

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

Hence height of tower is $20 \sqrt{3}$ meters.

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