sir this is the important question from the book -ML aggarwal( avichal publication) class 10th , chapter20 , heights and distances

it is given that 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 45 to 30.

Find the height of the tower and give your answer, correct to 1/10 of a metre.

question no 37 , heights and distances , ICSE board, ML Aggarwal

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 30

^{0}and 45^{0}In right triangle TAR

tan θ = TR/AR

Substituting the values

tan 30

^{0}= h/ (10 + x)So we get

1/√3 = h/ (10 + x)

h = (10 + x)/ √3 …. (1)

In triangle TBR

tan 45

^{0}= TR/BR = h/xSo 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.