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, 10:10 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, 10:16 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 $\displaystyle \sqrt{4^2 + 2^2 - 2(4)(2)cos(135)} = 5.6\ miles$

Now, to find the direction from which he is from the initial point is obtained using the sine rule. - Jun 20th 2010, 10:22 PMwinsome
can you give me its picture ?

- Jun 20th 2010, 10:35 PMUnknown008
Here it is:

Attachment 17948 - Jun 20th 2010, 10:41 PMwinsome
Thanks a lot