1. The problem asks for the length of the hypotenuse $c$ in a right triangle with legs 15 m and 8 m. 2. We use the Pythagorean theorem: $$c^2 = a^2 + b^2$$ where $a$ and $b$ are the legs of the triangle. 3. Substitute the given values: $$c^2 = 15^2 + 8^2 = 225 + 64 = 289$$ 4. Take the square root of both sides to find $c$: $$c = \sqrt{289} = 17$$ 5. Therefore, the length of the hypotenuse is 17 m. The correct answer is c 17 m.