An observer 2.25 m tall is 42.75 m away from a chimney. The angle of elevation o

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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?

Options:

A . 40 m

B . 35 m

C . 45 m

D . 50 m

Answer: Option C
:
C

The given situation is represented by the figure below:

In triangle ABE,
$tan 45^{\circ} = \frac{A B}{E B} A l s o, E B = D C ∴ t a n 45^{\circ} = \frac{A B}{D C} \Rightarrow A B = D C \times t a n 45^{\circ} \Rightarrow A B = 1 \times 42.75$
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.

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