1. **Problem statement:** We have three points: P, Q, and R. Q is 60 km due north of P, and R is 45 km due east of Q. We need to find the bearing of R from P. 2. **Understanding bearings:** Bearing is the direction measured clockwise from the north line. It is expressed in degrees from 0° to 360°. 3. **Set up the coordinate system:** Place P at the origin $(0,0)$. Since Q is 60 km north of P, Q is at $(0,60)$. Since R is 45 km east of Q, R is at $(45,60)$. 4. **Find the vector from P to R:** The vector PR has coordinates $(45 - 0, 60 - 0) = (45, 60)$. 5. **Calculate the bearing:** The bearing angle $\theta$ is measured clockwise from north. First, find the angle $\alpha$ between vector PR and the north direction (positive y-axis). Using the tangent function: $$\tan(\alpha) = \frac{\text{east displacement}}{\text{north displacement}} = \frac{45}{60} = 0.75$$ Calculate $\alpha$: $$\alpha = \arctan(0.75) \approx 36.87^\circ$$ 6. **Determine the bearing:** Since the vector is east of north, the bearing from P to R is: $$\text{Bearing} = 0^\circ + 36.87^\circ = 36.87^\circ$$ **Final answer:** The bearing of R from P is approximately $36.87^\circ$ measured clockwise from north.