The fastest way to find an obtuse triangle based on several sets of lengths

Question

A question from ACT math:

I'm wondering except using the law of cosine to get the answer K, is there any faster way to figure it out?

Answer 1

If $\angle A$ is an obtuse angle in a triangle.

$$90<\angle A<180, -1<\cos\angle A<0$$

$$\cos\angle A= \frac{b^2+c^2-a^2}{2bc} <0$$

using only numerator since denominator is always positive

$$a^2>b^2+c^2$$

where $a$ is the longest side

$$16^2>11^2+8^2$$