1. **State the problem:** A kite is flying with a string 150 feet long making a 45° angle with the ground. We need to find the height of the kite above the ground. 2. **Formula used:** We use the trigonometric relationship for a right triangle: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ where the opposite side is the height of the kite, the hypotenuse is the length of the string, and $\theta$ is the angle with the ground. 3. **Apply the formula:** Here, $\theta = 45^\circ$ and hypotenuse = 150 feet. $$\sin(45^\circ) = \frac{\text{height}}{150}$$ 4. **Solve for height:** $$\text{height} = 150 \times \sin(45^\circ)$$ 5. **Calculate $\sin(45^\circ)$:** $$\sin(45^\circ) = \frac{\sqrt{2}}{2}$$ 6. **Substitute and simplify:** $$\text{height} = 150 \times \frac{\sqrt{2}}{2} = \frac{150 \sqrt{2}}{2}$$ 7. **Simplify the fraction:** $$\text{height} = 75 \sqrt{2}$$ 8. **Approximate the value:** $$75 \times 1.414 = 106.05$$ **Final answer:** The kite is approximately 106.05 feet high.