Question

a tv tower stands vertically on the side of the road. from the point of other side directly opposite to the tower,the angle of elevation of the top of tower is 60°.from another point 10m away from this point on the line joining this point to the flore of the tower the angle of elevation of the top of the tower is 30° . find the hight of the tower and the weith of the road

Answer 1

Answer:

In this figure; CD=10m,∠ACB=60∘,∠ADB=30∘,AB=? and BD=?

In △ABC,

tan60∘=xh

3=xh

h=x3 --------- (1)

In △ABD,

tan30∘=10+xh

31=10+xh

h3=10+x ---------- (2)

From equation (1) and (2);

x3=310+x

3x=10+x

x=5

,which is the width of the road.

From (1),

h=53 m

,which is the height of the tower.