Question

Suppose a triangle has sides a, b, and c, and that a^2 + b^2 > c^2. Let theta be the measure of the angle opposite the side of length c. Which of the following must be true?

Answer 1

One way to determine is to imagine what triangle looks like, starting with \(a^2+b^2=c^2\)

If \(c^2\) is getting smaller, then we have \(a^2+b^2 > c^2\), right? Hypotenuse is getting smaller while leaving the two legs the same size. That pulls the two legs toward each other:

Answer 2

So we can see that we have acute triangle.

Answer 3

So is A. "Theta is an acute angle" the only answer?

Answer 4

Do you really think it is the only answer?

Answer 5

D, also?

Answer 6

and C?

Answer 7

Yeah, so that make B false.

And since \(\theta\) is acute ( \(0<\theta<\dfrac{\pi}{2}\) ), \(\cos\theta > 0\)

Answer 8

So answer is A, C, and D

Answer 9

Thanks for the help! :)

Answer 10

No problem