Check your dictionary.

Almost all will have a picture showing the compass points.

From your question, the NE bearing is 90 degrees to the SE bearing, thus you have a right angle.The distance back to the initial position is the square root of ( 3.5^2 + 8.2^2).

Even without a diagram you can visualize that the return bearing will be in the NorthWest quadrant.

It actually will be the NW bearing + the Arctan(3.5/8.2).

After you lookup and determine where the compass points are, you can simply graph (or draw) the lengths given [of course you should draw it to a reduced scale so that it will fit on a sheet of paper, as opposed to drawing the line 3.5 km long. The real problem with drawing the line to scale is the number of pencils required, but you are free to persue that method.]

3.5^2

3*3 = 9 and 4*4 = 16

3.5^2 is approximately halfway between 9 and 16 or about 12.

8.2^2

8*8 = 64 and 9*9 = 81, difference 81-64 = 17

0.2 or 1/5 * the difference of 17 is about 3

so 8.2^2 is about 67 = 64+3

67+12 = 79 which is about equal to 81.

Square root of 81 is 9

The returning distance is going to be about 9 km.

As for the bearing, 3.5 divided by 8.2 is roughly 1/2

The Arctan of 1 is 45 degrees, so half of that is 22 degrees.

That means the return bearing will be NW or 45 degrees + 22 degrees

orROUGHLY67 degrees West of North.

You can use a calculator to determine more precise values for the answer.