In `triangle ABC`, if `a=13,b=14` and `c=15` , then `sin.(A)/(2)=` ...................

Options

A. `(1)/(5)`
B. `sqrt((1)/(5))`
C. `(4)/(5)`
D. `(2)/(5)`

Explanation

Given `a=13,b=14,c=15`
`s=(a+b+c)/(2)`
`=(13+14+15)/(2)=(42)/(2)`
`=21`
`"sin"(A)/(2)=sqrt(((s-a)(s-c))/(bc))`
`sqrt(((21-14)(21-15))/(14xx15))`
`sqrt((7xx6)/(14xx15))`
`=sqrt((1)/(5))`
Hence, correct answer from the given alternatives is (b)