A sparrow flies 26 km at a bearing o \( 042^{\circ} \). It then flies 49 km due south and lands. How far south of its starting point does the sparrow land? Give your answer to 1 d.p.

To determine how far south the sparrow lands relative to its starting point, follow these steps: 1. **First Flight (26 km at Bearing \( 042^\circ \)):** - **Bearing Definition:** A bearing of \( 042^\circ \) means the direction is \( 42^\circ \) east of due north. - **South Component:** To find the southward component of this flight, use the sine function: \[ \text{South component} = 26 \times \sin(42^\circ) \] \[ \sin(42^\circ) \approx 0.6691 \] \[ \text{South component} \approx 26 \times 0.6691 \approx 17.4 \text{ km} \] 2. **Second Flight (49 km Due South):** - This flight directly adds to the southward displacement: \[ \text{Additional south component} = 49 \text{ km} \] 3. **Total Southward Displacement:** - Add the south components from both flights: \[ \text{Total south distance} = 17.4 \text{ km} + 49 \text{ km} = 66.4 \text{ km} \] **Final Answer:** The sparrow lands **66.4 km** south of its starting point.