Subjects trigonometry

Skyscraper Height

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Skyscraper Height


1. **State the problem:** Sadie is 1.69 meters tall and stands 275 meters from a skyscraper. She measures the angle of elevation to the top of the skyscraper as 36°. We need to find the height of the skyscraper. 2. **Formula used:** We use the tangent of the angle of elevation, which relates the height difference to the horizontal distance: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h - 1.69}{275}$$ where $h$ is the total height of the skyscraper. 3. **Calculate the height difference:** $$h - 1.69 = 275 \times \tan(36^\circ)$$ Calculate $\tan(36^\circ)$: $$\tan(36^\circ) \approx 0.7265$$ So, $$h - 1.69 = 275 \times 0.7265 = 199.79$$ 4. **Find the total height $h$:** $$h = 199.79 + 1.69 = 201.48$$ 5. **Final answer:** The height of the skyscraper is approximately **201.48 meters**. This matches the answer attempt provided, confirming the calculation is correct.