Question

finding side lengths find the unknown side length. simplify answers that are radicals. tell whether the side lengths form a pythagorean triple. 9. right triangle with hypotenuse 89, one leg 39, unknown leg x

Explanation:

Step1: Apply Pythagorean theorem

$$x^2 + 39^2 = 89^2$$

Step2: Calculate squared values

$$x^2 + 1521 = 7921$$

Step3: Isolate $x^2$

$$x^2 = 7921 - 1521 = 6400$$

Step4: Solve for $x$

$$x = \sqrt{6400} = 80$$

Step5: Check Pythagorean triple

All sides (80, 39, 89) are positive integers, so they form a Pythagorean triple.

Answer:

The unknown side length is 80, and the side lengths form a Pythagorean triple.