1. **State the problem:** We have a right triangle HGF with a right angle at G. The side HG measures 23 units, angle F is 71°, and we need to find side HF labeled as $x$. 2. **Identify the sides relative to angle F:** - Side HG (23 units) is adjacent to angle F. - Side HF ($x$) is the hypotenuse. 3. **Use the cosine function:** Cosine relates adjacent side and hypotenuse: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 4. **Set up the equation:** $$\cos(71^\circ) = \frac{23}{x}$$ 5. **Solve for $x$:** Multiply both sides by $x$: $$x \cos(71^\circ) = 23$$ Divide both sides by $\cos(71^\circ)$: $$x = \frac{23}{\cos(71^\circ)}$$ 6. **Calculate $\cos(71^\circ)$:** $$\cos(71^\circ) \approx 0.32557$$ 7. **Evaluate $x$:** $$x = \frac{23}{0.32557} \approx 70.63$$ 8. **Round to the nearest tenth:** $$x \approx 70.6$$ **Final answer:** $$\boxed{70.6}$$