Question

Example 3: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°. What is the height
of the chimney?
​

Answer 1

Given

• AC = chimney
• ED = observer
• ∠AEB = 45°
• EB = DC = 28.5 m
• ED = BC = 1.5 m

Find out

• Height of chimney

Solution

In ∆AEB

$\implies\sf tan\:45\degree=\dfrac{AB}{BE} \\ \\ \\ \implies\sf 1=\dfrac{AB}{28.5} \\ \\ \\ \implies\sf AB=28.5m \\ \\ \\ \therefore\bf {\underline{\red{Height\:of\:chimney}}} \\ \\ \implies\sf AC=AB+BC \\ \\ \\ \implies\sf AC=28.5+1.5 \\ \\ \\ \implies\sf AC=30m$

Hence, the height of chimney is 30m

$\rule{200}3$

Additional Information

• sin θ = perpendicular/base
• cos θ = base/hypothenuse
• tan θ = perpendicular/base

$\rule{200}3$

Answer 2

GIVEN:

• Height of Observer , DE = 1.5m

• Angle of elevation , D = 45°

• Distance of the observer , BE = 28.5m

TO FIND:

• Height of the chimney

SOLUTION:

Height of the chimney ,BC = AC + 1.5m

Therefore, AD = BE = 28.5m

=> Tan 45° = AC / AD

=> AC / 28.5 = 1

=> AC = 27.5m

As we know that,

Height of the chimney = AC + 1.5m

Height of the chimney = 28.5 + 1.5

Height of the chimney = 30m