Question

Suppose a triangle has sides a, b, and c, and that a^2 + b^2 < c^2. Let be the measure of the angle opposite the side of length c. Which of the following must be true?
***choose ALL that apply!!***

A. cos theta < 0

B. cos theta > 0

C. The triangle is not a right triangle.

D. a^2 + b^2 - c^2 = 2abcos theta

Answer 1

Answer:

  A, C, D are true

Step-by-step explanation:

The Law of Cosines tells you that D is true. The equation of D is a rearrangement of the usual presentation of the Law of Cosines.

The given relationship between the squares of the side lengths tells you that C is true. (The relation would be "equals" if the triangle were a right triangle.)

D being true, together with the given condition, tells you that 2ab·cos(θ) must be less than zero. Since the side lengths are positive, the cosine must be less than zero, making statement A true. (When A is true, B cannot be true.)