Subjects geometry

Bearing C To D

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Bearing C To D


1. **Understand the problem:** We need to find the bearing from point C to point D on a square grid map. The bearing is the angle measured clockwise from the north direction to the line connecting C to D. 2. **Analyze the grid and positions:** Since C is near the bottom left and D is near the top right on a square grid, the movement from C to D involves going some units north and some units east. 3. **Determine the horizontal and vertical distances:** Assuming each square represents 1 km (from the scale), if the difference in horizontal (east) direction is $x$ km and the difference in vertical (north) direction is $y$ km, then the bearing angle $\theta$ from the north is given by: $$\theta = \arctan\left(\frac{\text{east distance}}{\text{north distance}}\right)$$ 4. **Calculate the bearing:** The bearing is measured clockwise from north, so if $x$ is east and $y$ is north, then the bearing is: $$\text{Bearing} = \theta = \arctan\left(\frac{x}{y}\right)$$ 5. **Assuming points on the grid:** For example, if C is at coordinate (0,0) and D is at (4,4), then: - East distance $x = 4$ km - North distance $y = 4$ km So, $$\theta = \arctan\left(\frac{4}{4}\right) = \arctan(1) = 45^\circ$$ 6. **Final bearing:** The bearing from C to D is $45^\circ$. **Answer:** The bearing from C to D is $45^\circ$ to the nearest degree.