Question

find the length of the third side of the right triangle.
the length of the third side is
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle with hypotenuse $c$ and legs $a,b$, $a^2 + b^2 = c^2$. Here, $c=17$, $a=8$, so:
$$8^2 + b^2 = 17^2$$

Step2: Calculate squared values

Compute the squares of the known sides:
$$64 + b^2 = 289$$

Step3: Isolate $b^2$

Subtract 64 from both sides:
$$b^2 = 289 - 64 = 225$$

Step4: Solve for $b$

Take the positive square root (side length is positive):
$$b = \sqrt{225} = 15$$

Answer:

15