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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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