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.