1. **Problem statement:** You are standing 62 meters from a hot air balloon. The angle of elevation to the top of the balloon is 31°. Find the height of the balloon to the nearest tenth. 2. **Formula used:** We use the tangent function in right triangle trigonometry, which relates the angle of elevation $\theta$, the opposite side (height $h$), and the adjacent side (distance $d$): $$\tan(\theta) = \frac{h}{d}$$ 3. **Apply the formula:** Given $\theta = 31^\circ$ and $d = 62$ meters, solve for $h$: $$h = d \times \tan(\theta)$$ 4. **Calculate:** $$h = 62 \times \tan(31^\circ)$$ Using a calculator: $$\tan(31^\circ) \approx 0.6009$$ So, $$h = 62 \times 0.6009 = 37.2558$$ 5. **Round to the nearest tenth:** $$h \approx 37.3 \text{ meters}$$ **Final answer:** The height of the balloon is approximately **37.3 meters**.