When the suns altitude increases from 300 to 600 the length of the shadow of a tower decreases by 100 Metres find the height of the tower?

49.

A man standing in one corner of a square football field observes that the angle subtend by a pole in the corner just diagonally opposite to this corner is 60°. When he retires 80 m from the corner, along the same straight line, he finds the angle to be 30°. The length of the field is

• 20 m

• 

• 40 m

• 

D.

Let AB = BC = x metre,   

Solution:

In the figure

AB is the tower

BD and BC are the shadow of the tower in two situations

Consider BD = x m and AB = h m

In triangle ABD

tan 450 = h/x

So we get

1 = h/x

h = x ….. (1)

In triangle ABC

tan 300 = h/(x + 10)

So we get

1/√3 = h/(x + 10)

Using equation (1)

h√3 = h + 10

h (√3 – 1) = 10

We know that

h = 10/(√3 – 1)

It can be written as

h = [10 (√3 + 1)]/ [(√3 – 1) (√3 + 1)]

By further calculation

h = (10√3 + 1)/ 2

So we get

h = 5 (1.73 + 1)

h = 5 × 2.73

h = 13.65 m

Therefore, the height of the tower is 13.65 m.

When the sun's altitude changes from 30∘ to 60∘, the length of the shadow of a tower decreases by 70 m. What is the height of the tower?

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