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.

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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.
The sparrow lands **66.4 km** south of its starting point.

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.

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