Question

Suppose a triangle has sides a, b, and c, and that a2 + b2 < c2. Let θ be the measure of the angle opposite the side of length c. Which of the following must be true?

1. cosθ<0

2. cosθ>0

3. The triangle is not a right triangle.

4.a^2 + b^2 - c^2 = 2abcosθ

Answer 1

well its not a right triangle
and the Law of cosines is always true --> c^2 = a^2 +b^2 -2abcos theta
a longer c means the angle is greater --> theta>90 --> cos theta < 0