Exercise 17 Page 459

For the given triangles, we will find the range of possible values for x.

In order to do that, we will use the Hinge Theorem to compare the side lengths.

Applying the theorem, we can write an inequality for the side lengths. 57^(∘) > 41 ^(∘) ⇒ 12 > 3x-6 Let's solve the inequality for x.

All x-values less than 6 will work. In addition, 3x-6 must be greater than 0.

Therefore, 2^(∘) is the lower limit of x. We can determine the range of possible values of x by combining the two inequalities. We will rewrite x>2 as 2