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

Explanation

To solve the problem, we need to find the value of \( \sin A \sin B \sin C \) given that \( \tan A : \tan B : \tan C = 3 : 4 : 5 \).

### Step-by-Step Solution:

1. **Assign Values to Tangents**:
Let \( \tan A = 3k \), \( \tan B = 4k \), and \( \tan C = 5k \) for some constant \( k \).

2. **Use the Identity for Tangents in a Triangle**:
...