Geometry

Trigonometry

Medium

A 2 m tall boy is 30 m away from a tower. The angle of elevation of the top of the tower from his eye is 45°. What is the height of the tower?

30 m

28 m

32 m

34 m

✅ Correct Option: 3

The angle of elevation is measured from the boy's eye, not from the ground. The boy's eyes are at 2 m height.

Let h be the height of the tower above the boy's eye level.

The horizontal distance from the boy to the tower is 30 m, and the angle of elevation is 45°.

Using the tangent ratio:

$\tan(45°) = \frac{h}{30}$

Since $\tan(45°) = 1$ :

$1 = \frac{h}{30}$

$h = 30$ m

The total height of the tower is the height above eye level plus the boy's eye height:

Total height $= h + 2$

Total height $= 30 + 2$

Total height $= 32$ m

Therefore, the height of the tower is 32 m.

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A 2 m tall boy is 30 m away from a tower. The angle of elevation of the top of the tower from his eye is 45°. What is the height of the tower?

Solution

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