A village is 10 km on a bearing \( 050^{\circ} \) from a point O . Calculate how far the village is north of O .

To find how far the village is north of point O, we can use some trigonometry! First, note that a bearing of \( 050^{\circ} \) is \( 50^{\circ} \) measured clockwise from north. To find the northward component, we can use the cosine function: Northward distance = \( 10 \, \text{km} \cdot \cos(50^{\circ}) \). Calculating this gives us approximately \( 10 \cdot 0.6428 \approx 6.43 \, \text{km} \). So, the village is about 6.43 km north of point O! Now, if you ever find yourself confused with bearings, remember that taking a pause to draw a simple triangle can simplify things immensely! Align the north direction (upward) and measure \( 050^{\circ} \) from there. It visually breaks down how to apply cosine and sine in real-life navigation!