He went 4 miles to the west and again went 2 miles to north west. how many miles did he go from the initial point.

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- Jun 20th 2010, 11:10 PMwinsomeElevation
He went 4 miles to the west and again went 2 miles to north west. how many miles did he go from the initial point.

- Jun 20th 2010, 11:16 PMUnknown008
If you made a simple sketch, I'm sure you'll see it better. The two different paths he took make two lines, and the total distance he is from his initial point makes a third line. In all, they make a triangle.

Since you know the directions he took, you'll see that the angle between the first two sides is 90 + 45 = 135 degrees.

Then, use the cosine rule to find the length of the last side of the triangle, which gives

Now, to find the direction from which he is from the initial point is obtained using the sine rule. - Jun 20th 2010, 11:22 PMwinsome
can you give me its picture ?

- Jun 20th 2010, 11:35 PMUnknown008
Here it is:

Attachment 17948 - Jun 20th 2010, 11:41 PMwinsome
Thanks a lot