A 1.5 tall boy is standing at soe dustance from a 30m tall building . the angle of elevation from his eyes tot the top of the building increases from30 to 60as he waljs towards the building . find the distance he walked towards the building?

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A 1.5 tall boy is standing at soe dustance from a 30m tall building . the angle of elevation from his eyes tot the top of the building increases from30 to 60as he waljs towards the building . find the distance he walked towards the building?

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A 1.5 tall boy is standing at soe dustance from a 30m tall building . ...

Let AE is the Length of the building.

So AE = 30

Again BE = DF = 1.5

AB = AE - BE

= 30 - 1.5

= 28.5

Now in triangle ABC,

tan60 = AB/BC

=> √3 = 28.5/BC

=> BC = 28.5/√3

Again in triangle ABD

tan30 = AB/BD

=> 1/√3 = 28.5/BD

=> BD = 28.5*√3

=> BC + CD = 28.5√3

=> 28.5/√3 + CD = 28.5√3

=> CD = 28.5√3 - 28.5/√3

=> CD = (28.5*3 - 28.5)/√3

=> CD = 28.5(3-1)/√3

=> CD = (28.5*2)/√3

=> CD = 57/√3

=> CD = 57√3/(√3*√3) (Multiply √3 in numerator and denominator)

=> CD = 57√3/3

=> CD = 19√3

So the distance he walked towords building = 19√3 m

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