Question

A triangle has sides of length 2, 2, and 3. Which of the following is the measure of the obtuse angle of the triangle?

Answer 1

`97.18^(\circ)`

Explanation:

An obtuse angle in the triangle is opposite to the greatest side. The greatest side in the triangle with sides lengths 2, 2 and 3 is side with length 3. By the cosine rule,

`3^2=2^2+2^2-2\cdot 2\cdot 2\cdot \cos \alpha,\\ \\9=4+4-8\cos \alpha,\\ \\-8\cos \alpha=9-4-4=1,\\ \\\cos \alpha=-(1)/(8),\\ \\\alpha\approx 97.18^(\circ).`