Subjects trigonometry

Kite Angle Bce76E

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1. **State the problem:** A kite is flying at an altitude of 121 ft, and the string attached to it is 175 ft long. We need to find the angle of elevation $\theta$ that the string makes with the ground. 2. **Identify the right triangle:** The altitude of the kite is the opposite side to the angle $\theta$, the string is the hypotenuse, and the ground is the adjacent side. 3. **Use the sine function:** Since sine relates the opposite side and hypotenuse, we use: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{121}{175}$$ 4. **Calculate the sine value:** $$\sin(\theta) = \frac{121}{175} \approx 0.6914$$ 5. **Find the angle $\theta$:** Use the inverse sine function: $$\theta = \sin^{-1}(0.6914)$$ 6. **Calculate the angle:** $$\theta \approx 43.7^\circ$$ 7. **Answer:** The angle of elevation the string makes with the ground is approximately **43.7 degrees**.