Question

l will MARK BRAINLIST

from the top of the tower
60m high,the angle of depression of the top and the bottom of a vertical lamp post are observed to be 30°and 60° respectively find. the horizontal distance between the tower and the lamp post.the height of the lamp post

Answer 1

Heya

Here is your answer

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Let AB be the building 

And CD be the lamp post. While DE is the horizontal line parallel to the ground from the top of the lamp post to the building.

So in Triangle ABC,

AB=60m

θ=60°

tan θ = perpendicular /base

tan 60°= AB / BC

√3=60 / BC

BC = 60 / √3

On rationalising denominator, we get 

BC=60 * √3 /3

    =[20 * √3]m

Ans) Distance between building and lamp post =20 √3 cm 

                                                                  =20*1.732(√3=1.732)

                                                                  =34.64m

EBCD  is a rectangle , hence BC =ED

In Triangle AED

θ=30°

tan 30° = AE / ED

1 /√3  = AE / 20√3AE * √3 = 20√3AE = 20mAB = AE + EBEB =60 - 20=40m

Ans) Since EB = CD (EBCD being a rectangle)CD or Height of lamp post = 40m

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Hope this helped!!!

Happy to help :)