Question

In `triangleABC,` if a = 3, b = 4, c = 5, then sin 2B = ______.

Options

• `3/20`

• `1/50`

• `4/5`

• `24/25`

Answer 1

In `triangleABC,` if a = 3, b = 4, c = 5, then sin 2B = `underline(24/25)`.

Explanation:

Since, `cos B =(c^2+a^2-b^2)/(2ca)`

`=(25+9-16)/30`

`=3/5`

`therefore sin B=sqrt(1-cos^2B)`

`=sqrt(1-9/25)`

`=4/5`

∴ Sin 2B = 2sin B cos B

`=2*4/5*3/5`

`=24/25`