1. **State the problem:** Given polar coordinates $\theta = 115^\circ$ and $r = 25$, convert these to Cartesian coordinates $(x, y)$. 2. **Formula used:** The conversion from polar to Cartesian coordinates is given by: $$x = r \cos \theta$$ $$y = r \sin \theta$$ 3. **Important notes:** - The angle $\theta$ should be in degrees or radians consistently. Here, $\theta$ is in degrees. - Use a calculator or trigonometric tables to find $\cos 115^\circ$ and $\sin 115^\circ$. 4. **Calculate $x$:** $$x = 25 \times \cos 115^\circ$$ Using a calculator, $\cos 115^\circ \approx -0.4226$ $$x = 25 \times (-0.4226) = -10.565$$ 5. **Calculate $y$:** $$y = 25 \times \sin 115^\circ$$ Using a calculator, $\sin 115^\circ \approx 0.9063$ $$y = 25 \times 0.9063 = 22.6575$$ 6. **Final answer:** The Cartesian coordinates are approximately: $$\boxed{(x, y) = (-10.57, 22.66)}$$