1. **State the problem:** We need to find the width of the river, which is the horizontal distance between the surveyor and the pole. 2. **Identify the known values:** - Height of the pole: 3 m - Height of the optical device: 1.2 m - Angle of elevation: 8.5° 3. **Calculate the vertical height difference:** $$\text{height difference} = 3 - 1.2 = 1.8\text{ m}$$ 4. **Use the tangent function:** The tangent of the angle of elevation relates the opposite side (height difference) to the adjacent side (width of the river): $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{1.8}{\text{width}}$$ 5. **Solve for the width:** $$\text{width} = \frac{1.8}{\tan(8.5^\circ)}$$ 6. **Calculate the value:** Using a calculator, $$\tan(8.5^\circ) \approx 0.1494$$ So, $$\text{width} = \frac{1.8}{0.1494} \approx 12.05\text{ m}$$ **Final answer:** The width of the river is approximately **12.05 meters**. To draw this, sketch a right triangle with: - The horizontal side labeled as the width of the river (unknown). - The vertical side labeled as 1.8 m (height difference). - The angle of elevation 8.5° at the surveyor's position. - The hypotenuse representing the line of sight from the device to the top of the pole.