1.

The shadow of tower, when the angle of elevation of the sun is 45o is foube 10 m longer than when it was 60o. Find the height of tower.s.

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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