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Question

A TV tower stands vertically on the side of a road. From a point on the other side directly opposite to the tower, the angle of elevation of the top of tower is 60o. From another point 10m away from this point, on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30o.Find the height of the tower and the width of the road.

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Solution


Let AB be the tower of height h.
In this figure; CD=10m,ACB=60,ADB=30,AB=? and BD=?

In ABC,

tan60=hx

3=hx

h=x3 --------- (1)

In ABD,

tan30=h10+x

13=h10+x

h3=10+x ---------- (2)

From equation (1) and (2);

x3=10+x3

3x=10+x

x=5 which is the width of the road.

From (1),
Height of the tower h=53 m

1157648_1023575_ans_73fd3ea2d0d94fd1845de59e5fd87a59.png

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