1. **Problem statement:** Find $x$ in the triangle with angle $70^\circ$ and side length 15 adjacent to the angle, with $x$ as the hypotenuse. 2. **Formula used:** In a right triangle, the cosine of an angle is adjacent side over hypotenuse: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 3. **Apply formula:** Here, $$\cos(70^\circ) = \frac{15}{x}$$ 4. **Solve for $x$:** Multiply both sides by $x$ and divide both sides by $\cos(70^\circ)$: $$x \cancel{\cos(70^\circ)} = \frac{15}{\cancel{\cos(70^\circ)}}$$ $$x = \frac{15}{\cos(70^\circ)}$$ 5. **Calculate value:** Using $\cos(70^\circ) \approx 0.3420$, $$x = \frac{15}{0.3420} \approx 43.9$$ 6. **Final answer:** $x = 43.9$ (to 3 significant figures)