Question

To a man standing outside his house, the angles of elevation of the top and bottom of a window are 60° and 45° respectively. If the height of the man is 180 cm and if he is 5 m away from the wall, what is the height of the window? (√3 = 1.732)

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Answer 1

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Height of the window AB = hm

Height of the mem DD' = 180 cm

CD = 500 cm

from ∆BCD:

tan 45° = BC / DC

$1 = \frac{x}{500}$

$\color{red}500 = x$

from ∆ ACD:

tan 60° = AC / CD

$\sqrt{3} = \frac{h + x}{500}$

$500 \sqrt{3} = h + x$

$500 \sqrt{3} = h + 500$

$500 \sqrt{3} - 500 = h$

$500( \sqrt{3} - 1) = h$

$500(1.732 - 1) = h$

$500(0.732) = h$

$366 \: cm = h$

$3.66m \: = h$

Therefore,

Therefore,Height of the window = 3.66m