To determine how far north and east the bird is from its starting point, we can use trigonometry and the concept of vectors.
Step 1: Convert the given bearing of 35° into a vector. To do this, we can use the direction cosines, which represent the proportions of the vector in each coordinate direction. The direction cosines can be found using the following formulas:
- Cosine of the angle with the east direction (x-axis): cos(35°) = 0.819
- Cosine of the angle with the north direction (y-axis): sin(35°) = 0.574
So, the direction cosines of the vector are approximately 0.819 for the x-axis and 0.574 for the y-axis.
Step 2: Multiply the direction cosines by the distance traveled (5 km) to find the components of the vector in each direction.
- East component: 0.819 * 5 km = 4.095 km (approximately)
- North component: 0.574 * 5 km = 2.87 km (approximately)
Therefore, the bird's final position is approximately 4.095 km east and 2.87 km north of its starting point.