In a ` A B C ,` if `tanB :tanC=3:4:5,` then the value of `sinA sinB sinC` is equal to `2/(sqrt(5))` (b) `(2sqrt(5))/7` `(2sqrt(5))/9` (d) `2/(3sqrt(5))`

Options

A. `(2)/sqrt(5)`
B. `(2sqrt(5))/(7)`
C. `(2sqrt(5))/(9)`
D. `(2)/(3sqrt(5))`

Answer

B

Explanation

Let `tan A=3k,tanB=4k` and `tan C=5k`
Now, `tan A+tan B+tan C=tan A.tan B.tan C`,
`rArr 12k=60k^(3)`
`rArr k=(1)/sqrt(5)`
`therefore tanA=(3)/sqrt(5).tanB=(4)/sqrt(5)` and `tan C=sqrt(5)`
`therefore sin A=(3)/sqrt(14)sinB=(4)/sqrt(21)sinC=sqrt(3)/(sqrt(6))`
Hence, `sinA sin B. sin C=(2sqrt(5))/(7)`