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Question
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)`
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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