1. **State the problem:** We need to find the height $h$ of a lamppost, which forms a right triangle with a horizontal distance of 40 inches and an angle of 70° between the horizontal leg and the hypotenuse. 2. **Identify the trigonometric relationship:** In a right triangle, the sine of an angle is the ratio of the opposite side to the hypotenuse. Here, $h$ is opposite the 70° angle, and the adjacent side is 40 inches. 3. **Use the tangent function:** Since we know the adjacent side and want the opposite side, use the tangent function: $$\tan(70^\circ) = \frac{h}{40}$$ 4. **Solve for $h$:** Multiply both sides by 40: $$h = 40 \times \tan(70^\circ)$$ 5. **Calculate the value:** Using a calculator, $$\tan(70^\circ) \approx 2.747$$ So, $$h \approx 40 \times 2.747 = 109.88$$ 6. **Final answer:** The height of the lamppost is about 110 inches.