for the right triangles below, find the exact values of the side lengths c and b. if necessary, write your…

Explanation:

Step1: Solve for (c) in first triangle

In a 45 - 45 - 90 triangle, the legs are equal and if the length of a leg is (a), the hypotenuse (c) is given by (c = a\sqrt{2}). Here (a = 2), so (c=2\sqrt{2}).

Step2: Solve for (b) in second triangle

In a 30 - 60 - 90 triangle, if the shorter leg (opposite 30°) is (x), the longer leg (opposite 60°) is (x\sqrt{3}) and the hypotenuse is (2x). Here the shorter leg is 6, and (b) is the longer leg. So (b = 6\sqrt{3}).

Answer:

(c = 2\sqrt{2}) (b = 6\sqrt{3})