If the angle of elevation of the sun changes from 45^\circ \to 60^\circ , then the length of the shadow of a pillardecreases by 10m. The height of the pillar is:

SSC CHSL 15 Nov 2015 Shift 1 Paper

Question : 127 of 199

Marks: +1, -0

If the angle of elevation of the sun changes from

45° \to 60°

, then the length of the shadow of a pillardecreases by 10m. The height of the pillar is:

Solution:

Given : CD is the pillar and AB = 10 m
To find : Height of pillar =

h=?

Solution : In ∆ACD,
⇒

tan(45°) = {CD}/{AD}

⇒

1 = h/{x+10}

⇒

h =x+10

------(i)
Again, in ∆BCD,
⇒

tan(60°) = {CD}/{DB}

⇒

√3 = h/x

⇒

h=(h-10)√3

[Using (i)]
⇒

h = h√ 3 − 10√ 3

⇒

h( √3 − 1) = 10√ 3

⇒

h = {10√3}/{√3−1}

Rationalizing the denominator,we get :
⇒

h = {10 √3}/{√3−1 }× ( √3+1) /( √3+1)

⇒

h ={10 √3( √3+1)}/ (√3−1)

⇒

h = 5√ 3(√ 3 + 1)

⇒

h=5(3+√3)

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