1. **Problem statement:** A boat sails 8 km north from point P to Q, then 6 km west from Q to R. We need to find the bearing of R from P and the distance from P to R. 2. **Formula and rules:** - Distance between two points can be found using the Pythagorean theorem: $$d = \sqrt{(\Delta x)^2 + (\Delta y)^2}$$ - Bearing is measured clockwise from the north direction. - To find the bearing, use the angle $$\theta = \tan^{-1}\left(\frac{\text{west displacement}}{\text{north displacement}}\right)$$ and then convert to bearing. 3. **Calculations:** - North displacement = 8 km - West displacement = 6 km - Distance from P to R: $$d = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \text{ km}$$ 4. **Finding the bearing:** - Calculate angle $$\theta = \tan^{-1}\left(\frac{6}{8}\right) = \tan^{-1}(0.75) \approx 36.87^\circ$$ - Bearing is measured clockwise from north towards west, so bearing of R from P is: $$360^\circ - 36.87^\circ = 323^\circ$$ - Rounded to nearest degree: $$323^\circ$$ **Final answers:** - Distance from P to R is 10 km. - Bearing of R from P is 323°.