"towards" the Eastern direction? Why not just say East?
√(5^2 + 4^2) = √41 km @ NθE where
tanθ = 4/5
√(5^2 + 4^2) = √41 km @ NθE where
tanθ = 4/5
tan angle north of east = 5/4
so angle = 51.3 degrees N of E
Which is 90 - 51.3 = 38.7deg E of N or compass bearing of boy from start
Step 1: Visualize the boy's movement on a 2D coordinate system. Let's assume his starting point is at the origin (0, 0).
Step 2: Calculate the magnitude of the resultant using the Pythagorean theorem:
Resultant magnitude (a) = √((distance north)² + (distance east)²)
= √((5km)² + (4km)²)
= √(25km² + 16km²)
= √(41km²)
≈ 6.40 km
Therefore, the magnitude of the resultant is approximately 6.40 km (a ≈ 6.40 km).
Step 3: Determine the direction of the resultant using trigonometry:
Let θ be the angle between the resultant and the north direction.
tan(θ) = (distance east) / (distance north)
tan(θ) = (4km) / (5km)
θ = tan^(-1)(4/5)
θ ≈ 38.66°
Since the boy started running in the northern direction and then moved towards the eastern direction, the angle between the resultant and the north direction is 38.66 degrees.
Therefore, the magnitude of the resultant is 6.40 km (a ≈ 6.40 km), and its direction is approximately 38.66 degrees east of north (b ≈ 38.66°).