How far is it from its starting place, and what is its bearing from its starting place?

Question

A ship steams 45 miles due north, turns to a bearing of 45° and steams 25 miles, then turns south and steams 40

miles. How far is it from its starting place, and what is its bearing from its starting place?

Answer 1

So, it has gone 5 + 25/sqrt(2) N and 25/sqrt(2) E.  Figure out that bearing using trig.

Answer 2

It goes north 45 miles so is now 45 miles NORTH of its starting point.

Then it turns to a heading of 45 degrees,  which means it is going north east.   Figure it is now on the hypotenuse of a 45-45 right triangle.   The hypotenuse is 25 miles.  Square that and you get 625 miles.   Half that and you get 312.5 miles.  

Cube root of that is 17.68 miles,   meaning you are now 17.68 miles EAST and 62.68 miles NORTH of your starting point.  

The ship turns south which is 180 degrees and goes for 40 miles.   It is now 22.68 miles NORTH of your starting point and still 17.68 miles EAST.    Use those two figures in a right triangle,  one is the height,  the other is the width.  

22.68 squared = 514.38

17.68 squared =  312.5

add them together   816.88......square root is  28.58 miles from its starting point.  

This is easier to see if you draw it out on paper,  which is why ships,  even with computer navigation,  still have charts and compasses for the calculating courses.

Answer 3

You lost me at the 45 miles due north.