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 he is 5 m away from the wall, what is the length of the window?
8.65 m
2 m
2.5 m
3.65 m
Explanation:
Let AB be the man and CD be the window
Given that the height of the man, AB = 180 cm, the distance between the man and the wall, BE = 5 m,
$\angle$DAF = 45° , $\angle$CAF = 60°
From the diagram, AF = BE = 5 m
From the right $\triangle$ AFD,
tan45°=$\dfrac{DF}{AF}$
=>1=$\dfrac{DF}{5}$
DF = 5 ⋯(1)
From the right $\triangle$ AFC,
tan60°=$\dfrac{CF}{AF}$
=>√3=$\dfrac{CF}{15}$
CF =5√3 ...(2)
Length of the window
= CD = (CF - DF)
=5√3−5 [∵ Substituted the value of CF and DF from (1) and (2)]
=5(√3−1)=5(1.73−1)
=5×0.73=3.65 m
Let AB be the man and CD be the window
Given that the height of the man, AB = 180 cm, the distance between the man and the wall, BE = 5 m,
$\angle$DAF = 45° , $\angle$CAF = 60°
From the diagram, AF = BE = 5 m
From the right $\triangle$ AFD,
tan45°=$\dfrac{DF}{AF}$
=>1=$\dfrac{DF}{5}$
DF = 5 ⋯(1)
From the right $\triangle$ AFC,
tan60°=$\dfrac{CF}{AF}$
=>√3=$\dfrac{CF}{15}$
CF =5√3 ...(2)
Length of the window
= CD = (CF - DF)
=5√3−5 [∵ Substituted the value of CF and DF from (1) and (2)]
=5(√3−1)=5(1.73−1)
=5×0.73=3.65 m