the angle of elevation of the sun is 450 and the length of the shadow of 12 m high tree is ‘x’ find the value of x.​

Question

the angle of elevation of the sun is 450

and the length of the shadow of 12 m high tree is ‘x’ find the value

of x.​

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Camila 2 months 2021-10-09T19:26:12+00:00 1 Answer 0 views 0

Answers ( )

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    2021-10-09T19:27:46+00:00

    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=10m

    let us assume CA=x

    In triangle ACB,

    tan60°=opposite side  /adjacent side

    √3=h/AC

    √3=h/x

    x=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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