Trigonometry-18

From the top of a building 60 meters high, the angles of depression of the top and bottom of a

small tower are observed to be 30⁰ and 60⁰. Find the height of the tower.

Solution: Let the height of the tower TR = x m

BD is the building and BD = 60 m

In triangle RSD, SD/RS = tan 30⁰

(60 - x)/RS = 1/√3

RS = (60 - x) √3

In triangle TBD, BD/BT = tan 60⁰

BD = BT X √3

i.e. 60/√3 = BT

But BT = RS

Therefore, (60 - x) √3 = 60/√3

(60 - x) 3 = 60

180 - 3x = 60

x = 40

The height of the tower is 40 m