Answer :
Answer:
≈ 51.34°
Step-by-step explanation:
Given:
- A ship steams 4km due east from O and then 5 km due north - What is the bearing of its final position from o
Solution:
- 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.