a man standing on the top of a multi-storey building, which is 30m high, observes the angle of elevation of the top of a tower as 60 degrees and the angle of depression of the base of the tower as 30 degrees. Find the horizontal distance between the building and the tower. also find the height of the tower.

let the height of the building be CD = 30 m

let the height of the tower be AB = h m.

the angle of elevation of the top of the tower be ∠ACE= 60 deg

the angle of depression of the bottom of the tower be ∠ECD=30 deg

in the right angled triangle CEB ,

in the triangle AEC,

therefore the horizontal distance between the building and the tower is 51.9 m.

and the height of the tower is AB=AE+EB=90+30=120 m.

hope this helps you.

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