A ship steams 4km due east from O and then 5 km due north - What is the bearing of its final position from o

The ship travels 4 km east from O, so it reaches a point 4 km away from O in the eastern direction. Let's call this point A.
Then, it travels 5 km north from A, so it reaches a point 5 km away from A in the northern direction. Let's call this point B.
Now, we need to find the bearing of the final position B from O.

To do this, we can use the Pythagorean theorem to find the distance OB:

OB² = OA² + AB²

OB² = 4² + 5²

OB² = 16 + 25

OB² = 41

OB = √41 (approximately 6.4 km)

Now, we can use the tangent function to find the bearing of OB from O:

[tex] \sf tan(θ) = \frac{opposite \: side (AB)}{ adjacent \: side (OA)}[/tex]

tan(θ) = 5 / 4

θ = arctan(5/4)

θ ≈ 51.34°

So, the bearing of the final position B from O is approximately 051° (51.34°).

Note: The bearing is measured clockwise from the north direction.

A ship steams 4km due east from O and then 5 km due north - What is the bearing of its final position from o​