Question

In ΔABC, if a = 2, b = 3 and sin A = `2/3`, then ∠B = ______.

Options

• `π/2`

• `π/3`

• `π/4`

• `π/6`

Answer 1

In ΔABC, if a = 2, b = 3 and sin A = `2/3`, then ∠B = `underlinebb(π/2)`.

Explanation:

We use the Sine Rule:

`a/sin A = b/sin B`

Step 1: Substitute the value

`2/(2/3) = 3/sin B`

Step 2: Simplify left side

`2 xx 3/2 = 3`

So, `3 = 3/sin B`

Step 3: Solve for sin B

sin B = 1

Step 4: Find angle B

sin B = 1

⇒ B = `π/2`