1.

If in `triangle ABC`, with usual notations , `a=18,b=24,c=30`, then `sin.(A)/(2)` is equal toA. `(1)/(sqrt(5))`B. `(1)/(sqrt(10))`C. `(1)/(sqrt(15))`D. `(1)/(2sqrt(5))`

Answer» Correct Answer - B
In `DeltaABC`,
`a=18, b=24, c=30`
`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)/(sqrt(10))`
Hence, correct answer from the given alternatives is (b).


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