the lengths of two sides of a right triangle are 5 inches and 8 inches. what is the difference between the…

Explanation:

Step1: Determine two - case scenarios

We use the Pythagorean theorem (a^{2}+b^{2}=c^{2}), where (c) is the hypotenuse. Case 1: The two given sides are legs. Case 2: One of the given sides is the hypotenuse.

Step2: Calculate the third - side length when both given sides are legs

Let (a = 5) and (b = 8). Then (c=\sqrt{5^{2}+8^{2}}=\sqrt{25 + 64}=\sqrt{89}\approx9.4) inches.

Step3: Calculate the third - side length when 8 is the hypotenuse

Let (a = 5) and (c = 8). Then (b=\sqrt{8^{2}-5^{2}}=\sqrt{64 - 25}=\sqrt{39}\approx6.2) inches.

Step4: Calculate the difference between the two possible lengths

(9.4−6.2 = 3.2) inches.

Answer:

3.2 inches