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Home » In the adjoining figure, the shadow of a vertical tower on the level ground increases by 10 m, when the altitude of the sun changes from 450 to 300. Find the height of the tower and give your answer, correct to 1/10 of a metre.
In the adjoining figure, the shadow of a vertical tower on the level ground increases by 10 m, when the altitude of the sun changes from 450 to 300. Find the height of the tower and give your answer, correct to 1/10 of a metre.
ML Agarwal Heights and distances class 10 Maths
In the adjoining figure, the shadow of a vertical tower on the level ground increases by 10 m, when the altitude of the sun changes from 450 to 300. Find the height of the tower and give your answer, correct to 1/10 of a metre.

Solution:

Consider TR as the tower where TR = h

BR = x

AB = 10 m

Angles of elevation from the top of the tower at A and B are 300 and 450

In right triangle TAR

tan θ = TR/AR

Substituting the values

tan 300 = h/ (10 + x)

So we get

1/√3 = h/ (10 + x)

h = (10 + x)/ √3 …. (1)

In triangle TBR

tan 450 = TR/BR = h/x

So we get

1 = h/x

x = h ….. (2)

Using both the equations

h = (10 + h)/ √3

√3h = 10 + h

By further calculation

√3h – h = 10

(1.732 – 1) h = 10

0.732 h = 10

h = 10/0.732 = 13.66

Hence, the height of the tower is 13.7 m.

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