Subjects geometry

Slide Angle 844137

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1. **State the problem:** We need to find the angle $\theta$ that the slide makes with the ground. The slide forms a right triangle where the height is 107 cm and the hypotenuse (slide length) is 250 cm. 2. **Formula used:** In a right triangle, the sine of the angle $\theta$ is the ratio of the opposite side (height) to the hypotenuse: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{107}{250}$$ 3. **Calculate sine value:** $$\sin(\theta) = 0.428$$ 4. **Find the angle $\theta$:** Use the inverse sine function: $$\theta = \sin^{-1}(0.428)$$ 5. **Evaluate the angle:** $$\theta \approx 25.4^\circ$$ 6. **Round to nearest degree:** $$\theta \approx 25^\circ$$ **Answer:** The slide makes an angle of approximately $25^\circ$ with the ground.