Question

If the shadow of a tower is 30 m long, when the sun's elevation is 30 degrees. what is the length of the shadow ,when sun's elevation is 60 degree?

Answer 1

Let AB(h ) be the height of the tower when angle of elevation of sun is 30° and BD be the shadow of a tower the angle of elevation of Sun is 60°. BC = 30 m , angle ACB =30° , Angle ADB= 60° Let AB = h m & BD = x m

In ∆ ABC

tan 30 ° = Perpendicular/base= BC /AB

tan 30° = BC/AB = h /30

1/√3= h/30

h= 30/√3………………(1)


In ∆ ABD


tan 60 ° = Perpendicular/base= AB/BD

tan 60° = h /x

√3 = (30/√3)/x ( from eq 1)

√3x= 30/√3

x= 30/ √3×√3 = 30 /3= 10

x= 10 m

Hence, the length of the shadow of tower,when sun's elevation is 60° is 10 m

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Hope this will help you...

Answer 2

perpendicular= Opposite side to angle theta

base=a=adjacent side to angle theta