1. **State the problem:** We have a straight line P–S–R with PS = 8.4 cm and a right angle at S (angle PSQ = 90°). Given angles QPS = 38° and SQR = 44°, we need to find the length QR. 2. **Analyze the figure and known angles:** Since PSR is a straight line, angle PSR = 180°. 3. **Use triangle PSQ:** Triangle PSQ is right-angled at S, with PS = 8.4 cm and angle QPS = 38°. 4. **Find length QS using trigonometry:** $$\tan(38^\circ) = \frac{QS}{PS} \implies QS = PS \times \tan(38^\circ) = 8.4 \times \tan(38^\circ)$$ Calculate: $$QS = 8.4 \times 0.7813 = 6.56 \text{ cm (approx)}$$ 5. **Find length SR:** Since PSR is a straight line and S is between P and R, let SR = x. 6. **Use triangle SQR:** Angle SQR = 44°, angle at Q is unknown, but triangle SQR has right angle at S (since QS is vertical and PSR is horizontal), so angle QSR = 90°. 7. **Use sine rule in triangle SQR:** In triangle SQR, angle SQR = 44°, angle QSR = 90°, so angle QRS = 46° (since angles sum to 180°). 8. **Use sine rule:** $$\frac{QR}{\sin(90^\circ)} = \frac{QS}{\sin(46^\circ)}$$ So, $$QR = \frac{QS \times \sin(90^\circ)}{\sin(46^\circ)} = \frac{6.56 \times 1}{0.7193} = 9.12 \text{ cm (approx)}$$ 9. **Final answer:** $$\boxed{QR = 9.12 \text{ cm}}$$ Answer correct to 3 significant figures is 9.12 cm.