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Applications of Trigonometry
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17/06/2021 11:09 am
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A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.
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17/06/2021 11:11 am
The distance boy walked towards the building i.e. XY
From figure,
XY = CD.
Height of the building = AZ = 30 m.
AB = AZ – BZ
= 30 – 1.5
= 28.5
Measure of AB is 28.5 m
In right ΔABD,
tan 30° = AB/BD
1/√3 = 28.5/BD
BD = 28.5√3 m
Again,
In right ΔABC,
tan 60° = AB/BC
√3 = 28.5/BC
BC = 28.5/√3 = 28.5√3/3
Therefore, the length of BC is 28.5√3/3 m.
XY = CD = BD – BC = (28.5√3-28.5√3/3)
= 28.5√3(1-1/3) = 28.5√3 × 2/3
= 57/√3 m.
Thus, the distance boy walked towards the building is 57/√3 m.