Question

Suppose a triangle has sides a, b, and c, and that a2 + b2 < c2. Let be the measure of the angle opposite the side of length c. Which of the following must be true? Check all that apply.
A. is an acute angle.
B. The triangle is not a right triangle.
C. cos < 0
D. The triangle is a right triangle.

Answer 1

We are given a triangle with sides corresponding to a, b and c. If this is a right triangle, then b being the longest side, the triangle's sides follow the Pythagorean theorem that states c2 = a2 + b2. In this case,  the problem states a2 + b2 < c2. we can assume values and use cosine law. theta then is greater than 90 degrees which is an obtuse angle. In this case, cos theta is negative. The conditions that apply are A, C and D