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°. What is the height of the chimney?

Options

• 40 m

• 50 m

• 45 m

• 35 m

Answer 1

45 m

Explanation:

The given situation is represented by the figure above:

In triangle ABE,

`"tan"  45^circ = "AB"/"EB"`

Also, EB = DC

`therefore "tan"  45^circ = "AB"/"DC"`

`=> "AB" = "DC" xx "tan"  45^circ`

`=> "AB" = 1 xx 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"`.