Subjects trigonometry

Cliff Height 25193A

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1. **State the problem:** We need to find the height of a vertical cliff given the angle of elevation to the top is 25 degrees from a point 235 meters away from the base. 2. **Formula used:** The height $h$ of the cliff can be found using the tangent of the angle of elevation: $$\tan(\theta) = \frac{\text{height}}{\text{distance}}$$ where $\theta = 25^\circ$ and distance = 235 m. 3. **Apply the formula:** $$\tan(25^\circ) = \frac{h}{235}$$ 4. **Solve for $h$:** $$h = 235 \times \tan(25^\circ)$$ 5. **Calculate the value:** Using a calculator, $$\tan(25^\circ) \approx 0.4663$$ 6. **Final height:** $$h = 235 \times 0.4663 = 109.56$$ So, the height of the cliff is approximately 109.56 meters.