Question

Suppose a triangle has sides a, b, and c with side c the longest side, and that a2 + b2 > c2. Let theta be the measure of the angle opposite the side of length c. Which of the following must be true? More than one can apply.

A. theta is an acute angle.
B. The triangle is not a right triangle.
C. The triangle in question is a right triangle.
D. cos theta < 0

Answer 1

B

Answer 2

by law of cosine, \[\cos \theta = \frac{a^2+b^2-c^2}{2ab}\]
because \(a^2+b^2>c^2\), the numerator in the fraction is positive

this means the angle is acute

Answer 3

B and A

Answer 4

B and A