Question

In ΔABC, if a = 2, b = 3, c = 4, then prove that the triangle is obtuse angled.

Answer 1

Given: a = 2, b = 3, c = 4

∴ Side AB is the largest.

Hence, ∠C is the largest angle.

By cosine rule, cos C = `(a^2 + b^2 - c^2)/(2ab)`

∴ cos C = `(4 + 9 - 16)/(2(2)(3))`

= `(-3)/12`

= `- 1/4`

Since cos C is negative, ∠C is obtuse.

∴ ΔABC is an obtuse angled triangle.