The shadow of a vertical tower on a level ground increased by 10m when the altitude of a sun changes from an angle of elevation 45° to 30° . Find the height of a tower .
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Let
Height of tower = h
BC = x
BD = BC + CD = x + 10
In ∆ABC
P/B = AB/BC = tan 45°
h/x = 1
h = x ===> eqn 1
In ∆ABD
AB/BD = tan 30°
h / x + 10 = 1 / √3
√3 h = h + 10 [ :. from eqn 1 ]
3h - h = 10
h ( √3 - 1 ) = 10
h = 10 / √3 - 1 × √3 + 1 / √3 + 1
h = 10 √3 + 10 / ( √3 )² - ( 1 )²
h = 10 ( √3 + 1 ) / 3 - 1
h = 10 ( √3 + 1 ) / 2
h = 5 ( √3 + 1 )
h = 5 ( 1.73 + 1 )
h = 5 ( 2.73 )
h = 13.65
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