Geometry

Trigonometry

Medium

An observer, 1.5 m tall, is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. Determine the height of the chimney?

6.5 m

15.5 m

28.5 m

30 m

✅ Correct Option: 4

The observer's height is 1.5 m, standing 28.5 m away from the chimney. The angle of elevation from her eyes to the top of the chimney is 45°.

The angle is measured from the observer's eye level, not from the ground.

The total height of the chimney consists of two parts:

Height above eye level (h)
Observer's eye level height (1.5 m)

From the observer's eyes, a right triangle is formed with:

Horizontal distance = 28.5 m
Angle of elevation = 45°
Opposite side = h (height above eye level)

$\tan(45°) = \dfrac{h}{28.5}$

Since $\tan(45°) = 1$ :

$1 = \dfrac{h}{28.5}$

$h = 28.5$ m

Total height of chimney = Height above eye level + Observer's height

Total height $= 28.5 + 1.5$

Total height $= 30$ m

Therefore, the height of the chimney is 30 m.

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An observer, 1.5 m tall, is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. Determine the height of the chimney?

Solution

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