Question

the angle of elevation and depression of the top and the bottom of a tower from the top of the building 60m high are 30 degree and 60 degree respectively .find the diffrence between the heights of the building and the tower and the distance betweeen them

Answer 1

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Let the height of the building be AB = 60 metre

Let the height of the tower be CD = h metre

Hence,

distance between building and the light house be BD.

in the ∆ ABD,

tan 60°=AB/BD

√3=60/BD

BD√3=60

BD=(60/√3)×(√3/√3)

BD=20√3

BD=20×1.732

BD=34.6

in the ∆ AEC,

tan 30°=AE/AC

1/√3=AE/20√3

AE=20×√3/√3

AE=20 m

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Hence,

the difference between the heights is AE =20 m.

the distance between the building and the tower is 34.6 m.

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