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If in ∆ABC with usual notations a = 18, b = 24, c = 30 then sin A/2 is equal to - Mathematics and Statistics

If in ∆ABC with usual notations a = 18, b = 24, c = 30 then sin A/2 is equal to

(A) `1/sqrt5`

(B) `1/sqrt10`

(C) `1/sqrt15`

(D) `1/(2sqrt5)`

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Solution

(B) `1/sqrt10`

`s=(a+b+c)/2=(18+24+30)/2=36`

`sin(A/2)=sqrt(((s-b)(s-c))/(bc))=sqrt(((36-24)(36-30))/(24xx30))=sqrt((12xx6)/(24xx30))=1/sqrt10`

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