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two men on opposite sides of a TV tower of height 20m notice the angle of elevation of the top of the tower to be 45° and 60° respectively. find the distance in meters between the two men.

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The man on the 45 degrees side:

Tan(45) = Opp / Adj (rearranging we get . . .)
Adj = Opp / Tan(45) = 20 / 1 = 20m

The man on the 60 degrees side:

Tan(60) = Opp / Adj (rearranging we get . . .)
Adj = 20 / Tan(60) = 20 / 1.732 = 11.547m

Therefore the distance between the two men is 20 + 11.547 = 31.547m