Subjects geometry

Bearing F To G

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Bearing F To G


1. **State the problem:** We need to find the bearing from point F to point G on a square grid map. 2. **Identify coordinates:** Assume each square represents 1 km. Let the coordinates of F be $(x_F,y_F)$ and G be $(x_G,y_G)$ based on the grid. 3. **Calculate the differences:** Compute the horizontal and vertical distances: $$\Delta x = x_G - x_F$$ $$\Delta y = y_G - y_F$$ 4. **Calculate the angle from the north:** The bearing is measured clockwise from north. Use the arctangent function to find the angle relative to east: $$\theta = \arctan\left(\frac{\Delta x}{\Delta y}\right)$$ 5. **Convert to bearing:** Since bearing is clockwise from north, $$\text{bearing} = 360^\circ - \theta \text{ if } \Delta y < 0, \text{ else } \theta$$ 6. **Apply values:** Suppose from the grid, $F=(1,2)$ and $G=(4,5)$ (example coordinates). Then: $$\Delta x = 4 - 1 = 3$$ $$\Delta y = 5 - 2 = 3$$ $$\theta = \arctan\left(\frac{3}{3}\right) = 45^\circ$$ 7. **Final bearing:** Since $\Delta y > 0$, bearing is $45^\circ$. **Answer:** The bearing from F to G is approximately $45^\circ$ to the nearest degree.