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Question

A person observed the angle of elevation of the top of a tower as 30°. He walked 50 m towards the foot of the tower along level ground and found the angle of elevation of the top of the tower as 60°. Find the height of the tower.

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Solution

Let be the tower of height. And person makes an angle of elevation of top of tower is 30°, he walks m towards the foot of tower then makes an angle of elevation 60°

Let , , and ,

Now we have to find height of tower.

We have the corresponding figure as follows

So we use trigonometric ratios.

In a triangle ABC,

Again in a triangle,

3h=h3+503h=h+5032h=503h=253h=25×1.73h=43.25

Hence the height of tower is .


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