1. **State the problem:** We need to find the length $x$ of the hypotenuse in a right triangle where one leg is 23 m and the angle adjacent to the base is 59°. 2. **Identify the sides and angle:** The side of length 23 m is opposite the 59° angle, and $x$ is the hypotenuse. 3. **Formula used:** In a right triangle, the sine of an angle is the ratio of the opposite side to the hypotenuse: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 4. **Apply the formula:** Here, $\theta = 59^\circ$, opposite side = 23 m, hypotenuse = $x$. $$\sin(59^\circ) = \frac{23}{x}$$ 5. **Solve for $x$:** $$x = \frac{23}{\sin(59^\circ)}$$ 6. **Calculate $\sin(59^\circ)$:** $$\sin(59^\circ) \approx 0.8572$$ 7. **Find $x$:** $$x = \frac{23}{0.8572} \approx 26.8$$ **Final answer:** The hypotenuse $x$ is approximately 26.8 meters.