Question

The angle of elevation of the top of a chimney from the foot of a tower is 60° and the angle of depression of the foot of the chimney from the top of the tower is 30°. If the height of the tower is 40 meters, find the height of the chimney. Also, find the length of the wire tied from the top of the chimney to the top of the tower.

Answer 1

Let BA be the Chimney and CD be the tower.

In ΔCBD,

tan 30° = `40/(BC)`

⇒ BC = `40sqrt(3)  m`

In ΔABC,

tan 60° = `(AB)/(40sqrt(3))`

⇒ AB = 120 m

AE = (120 – 40) m = 80 m, 

ED = BC = `40sqrt(3)` m

Now, AD = `sqrt(AE^2 + ED^2)`

= `sqrt(80^2 + (40sqrt3)^2)`

= `sqrt(6400 + 40^2 xx 3)`

= `sqrt(6400 + 1600 xx 3)`

= `sqrt(6400 + 4800)`

= `sqrt(11200)`

= `40sqrt(7)` m

Thus, length of wire tied from the top of the chimney to the top of tower is `40sqrt(7)` m.