1.

ple 3 The shadow of a tree is found to be 6 m longer whenthe sun's elevation is 45° than when it is 60°. Find the height

Answer»

Let AB be the tower with height h.Let AC and AD be the shadows when elevation of sun are 60 degrees and 45 degrees.As per given, CD=10mlet us assume CA=xIn triangle ACB,tan60°=opposite side /adjacent side√3=h/AC√3=h/xx=h/√3 ------ equation (1)

In traingleDAB,

tan45°=AB/AD=h/(AC+DC)1=h/(x+10)x+10=h-----equation(2)

By substituting the value of x in equation 2 we get:

h/√3+10=h

h-h/√3=10

h√3-h=10√3

h(√3-1)=10√3

h=10√3/√3-1

Rationalizing factor is√3+1

h=10√3(√3+1)/[(√3-1)x(√3+1)]

h=10√3(√3+1)/(3-1)

h=10√3(√3+1)/2

h=5√3(√3+1) m

h=5(3+√3)

=15+5*√3

=15+5*1.732

=15+8.660

=23.66 m

∴ Height of tower is 23.66m

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