I'm a bit rusty on how bearings work. Can't seem to visualize it or draw a picture. Please explain the method for me, please! This is the problem:

A ship leaves port at a bearing of N 80 degrees E with an average speed of five knots. After one hour the ship turns 90 degrees to the southwest and travels for two or more hours at an average speed of 15 knots. Find the distance the ship is from the port after three hours and its bearing with respect to the initial port.

2. Originally Posted by Gambit
...This is the problem:

A ship leaves port at a bearing of N 80 degrees E with an average speed of five knots. After one hour the ship turns 90 degrees to the southwest (do you mean southeast?) and travels for two or more hours at an average speed of 15 knots. Find the distance the ship is from the port after three hours and its bearing with respect to the initial port.

1. Draw a sketch.

2. You are dealing with a right triangle whose legs are $\displaystyle a = 5$ and $\displaystyle b = 30$ . Use Pythagorean theorem to calculate the distance between port and the position after the 3 hours journey:

$\displaystyle d = \sqrt{5^2+30^2} = \sqrt{925}\approx 30.4138...nm$

3. Calculate the angle at P in the right triangle. Use the tan-function:

$\displaystyle \tan(\alpha) = \frac{30}5=6~\implies~\alpha \approx 80.5377^\circ$

Add this angle to the initial bearing to get the final bearing $\displaystyle \beta$:

$\displaystyle \beta = 80^\circ + 80.5377^\circ = 160.5377^\circ$

3. I think you're right; my teacher must mean southeast. That was one part that was confusing me the most. Thanks a lot!