Question

The smallest angle of the ΔABC, when a = 7, b = `4sqrt(3)` and c = `sqrt(13)` is ______.

Options

• 30°

• 15°

• 45°

• 90°

Answer 1

The smallest angle of the ΔABC, when a = 7, b = `4sqrt(3)` and c = `sqrt(13)` is 30°.

Explanation:

Since, c = `sqrt(13)` is the smallest side.

∴ c is the smallest angle.

∴ cos c = `("b"^2 + "a"^2 - "c"^2)/(2"ab") = (48 + 49 - 13)/(2 xx 7 xx 4sqrt(3))`

⇒ cos c = `3/(2sqrt(3)) = sqrt(3)/2`

⇒ c = 30°