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?

30 m

The correct answer is Option (4) → 30 m

Let the height of the chimney be $h$ meters.

Given:

• Height of observer = 1.5 m
• Distance from observer to chimney = 28.5 m
• Angle of elevation from eye-level = $45^\circ$

From the observer's eye-level, the vertical height to the top of the chimney is $(h - 1.5)$ m.

Using the tangent ratio in a right triangle:

$\tan(45^\circ) = \frac{h - 1.5}{28.5}$

$1 = \frac{h - 1.5}{28.5}$

$h - 1.5 = 28.5$

$h = 28.5 + 1.5 = 30$