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

Answer:

$97.18^{\circ}$

Step-by-step 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,

$3^2=2^2+2^2-2\cdot 2\cdot 2\cdot \cos \alpha,\\ \\9=4+4-8\cos \alpha,\\ \\-8\cos \alpha=9-4-4=1,\\ \\\cos \alpha=-\dfrac{1}{8},\\ \\\alpha\approx 97.18^{\circ}.$