A ship is sailing on a bearing of SE. It changes direction and sails on a bearing of NE. Through what angle did it turn?

Question

A ship is sailing on a bearing of SE. It changes direction and sails on a bearing of NE. Through what angle did it turn?

 

Answer 1

Hi Young--

 

The short answer is 90 degrees.

 

The long answer is that the 4 cardinal directions on a compass (N, E, S, W) cover the 360 degrees of a circle, with 90 degrees in between each one. The 4 ordinal directions (NE, SE, SW,NW) each fall exactly halfway between 2 of the cardinal directions, or 45 degrees from them. For example, NE is 45 degrees from N, and 45 degrees from E. Do the same with the other ordinals, and you'll see that the difference between each ordinal and the next is also 45 + 45, or 90 degrees.

 

Draw a big plus sign in the middle of your paper--you've just drawn a compass. Label the top end of the vertical axis N, then the right one E, the bottom S, and the left W. See how the 2 axes form 90 degree angles?

 

Now draw a circle around the plus sign so it looks like a pizza cut in 4ths. Then make 2 diagonal cuts to cut the pizza in 8ths, Between N and E, label the end of that cut "NE," and then fill in the remaining ordinals

 

If you were to take out the slices that NE to E, and E to SE, you'd be taking out 1/4 of the pizza, or 1/4 of the 360 degree circle. 1/4 of 360 = 90 degrees.

 

Hope this helps!

 

Matt