Question

In a triangle ABC, b = `sqrt3`, c = 1 and ∠A = 30°, then the largest angle of the triangle is ______ 

Options

• 135°

• 90°

• 60°

• 120°

Answer 1

In a triangle ABC, b = `sqrt3`, c = 1 and ∠A = 30°, then the largest angle of the triangle is 120°.

Explanation:

We have, b = `sqrt3`, c = 1 and ∠A = 30°

cos A = `(b^2 + c^2 - a^2)/(2bc)`

⇒ `sqrt3/2 = ((sqrt3)^2 + 1^2 - a^2)/(2sqrt3 . 1)`

⇒ a = 1, b = `sqrt3`, c = 1

∴ b is the largest side. Therefore, the largest angle B is given by

cos B = `(a^2 + c^2 - b^2)/(2ac) = (1 + 1 - 3)/(2.1.1) = -1/2 = cos 120^circ`

⇒ B = 120°