If in `triangle ABC`, with usual notations , `a=18,b=24,c=30`, then `sin.(A)/(2)` is equal to

Options

A. `(1)/(sqrt(5))`
B. `(1)/(sqrt(10))`
C. `(1)/(sqrt(15))`
D. `(1)/(2sqrt(5))`

Answer

B

Explanation

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).