1. **Problem statement:** We have two right triangles sharing an angle of 15°. The top-right triangle has hypotenuse $r=75$ and height $x$. We want to find $x$. 2. **Formula used:** In a right triangle, the side opposite an angle $\theta$ is related to the hypotenuse $r$ by the sine function: $$x = r \sin(\theta)$$ 3. **Apply the formula:** Here, $\theta = 15^\circ$ and $r = 75$, so $$x = 75 \sin(15^\circ)$$ 4. **Calculate $\sin(15^\circ)$:** Using a calculator or sine table, $$\sin(15^\circ) \approx 0.2588$$ 5. **Find $x$:** $$x = 75 \times 0.2588 = 19.41$$ 6. **Answer:** The height $x$ is approximately $19.41$ units.