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. 35 m
• B. 40 m
• C. 45 m
• D. 50 m

Answer 1

The correct option is C

45 m

The given situation is represented by the figure above
$\therefore tan{45}^{\circ }=\frac{AB}{EB}$
But EB = DC
$\therefore tan{45}^{\circ }=\frac{AB}{DC}\Rightarrow DC\times tan{45}^{\circ }=AB\Rightarrow AB=1\times 42.75$
Height of chimney = AC = AB + BC
But BC = ED $\therefore$ AC = AB + ED = 42.75 + 2.25 = 45m