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

wehave the information that The shadow of a vertical tower on a level ground increases by 10 m

when the altitude of the sun changes from 450 to 300.

wehave to Find the height of the tower, correct to two decimal places. please solve this providing figure

question no 18 , heights and distances , ICSE board

deepaksoniGuru

# The shadow of a vertical tower on a level ground increases by 10 m when the altitude of the sun changes from 450 to 300. Find the height of the tower, correct to two decimal places.

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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 45

^{0}Â = h/xSo we get

1 = h/x

h = x â€¦.. (1)

In triangle ABC

tan 30

^{0}Â = h/(x + 10)So we get

1/âˆš3 = h/(x + 10)

Using equation (1)

hâˆš3 = h + 10

h (âˆš3 â€“ 1) = 10

We know that

h = 10/(âˆš3 â€“ 1)

It can be written as

h = [10 (âˆš3 + 1)]/ [(âˆš3 â€“ 1) (âˆš3 + 1)]

By further calculation

h = (10âˆš3 + 1)/ 2

So we get

h = 5 (1.73 + 1)

h = 5 Ã— 2.73

h = 13.65 m

Therefore, the height of the tower is 13.65 m.