Question

An observer 2.25 m tall is 42.75 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is ${45}^{\circ }$. What is the height of the chimney?

• A. 40 m
• B. 35 m
• C. 45 m
• D. 50 m

Answer 1

The correct option is C

45 m

The given situation is represented by the figure below:


In triangle ABE,
$\tan {45}^{\circ }=\frac{AB}{EB}Also,EB=DC\therefore tan{45}^{\circ }=\frac{AB}{DC}\Rightarrow AB=DC\times tan{45}^{\circ }\Rightarrow AB=1\times 42.75$

Hence, the height of the chimney = AC = AB + BC
We can observe that BC = ED.
Thus, AC = AB + ED
= 42.75 + 2.25
= 45 m.