Expert: Sherman D. - 11/26/2006

Question
I miss this class and cant figure it out.

A person leaves home and walks 2 miles due west, then walks 3 miles southwest, finally walks 4 miles southeast.
How far away from home is she?

Answer
I prefer to draw this out. If you notice it looks like a trapezoid

Here is how you do it, if you make a dashed like connecting the Starting Point to the Finishing Point, then make a dashed line from the 2nd point to the finishing poing you get 2 triangles, now use this formula to find out the rest. Also assuming she traveled perfectly southwest/south east which would be 135 degrees leaving the others at 45 degrees, then

c^2 = a^2 + b^2 - 2ab(cos(C))

c^2 = 3^2 + 4^2 - 2(3 * 4)cos(135)
c^2 = 9 + 16 - 2(12)(-sqrt(2)/2)
c^2 = 25 + (24sqrt(2)/2)
c^2 = 25 + 12sqrt(2)
c = sqrt(25 + 12sqrt(2))

Now using that, you have

a^2 = b^2 + c^2 - 2bc(cosA)
a^2 = 2^2 + (sqrt(25 + 12sqrt(2))^2 - 2(2 * sqrt(25 + 12sqrt(2))cos(45)

a^2 = 4 + 25 + 12sqrt(2) - 2(2sqrt(25 + 12sqrt(2))(sqrt(2)/2))

a^2 = 29 + 12sqrt(2) - 2(2sqrt(2(25 + 12sqrt(2)))/2)
a^2 = 29 + 12sqrt(2) - 2sqrt(50 + 24sqrt(2))
a = about 5.258 miles

Info found at www.math.com/tables/trig/identities.htm

The answer to me seems right, because you know its going to be over 3 miles, but just to be on the safe side, if you go to answers.yahoo.com, click on Ask, then type in Need Help On Vectors, type in your problem, then click on Science and Mathematics, then click on Mathematics if it isn't already listed, then click send, and you should recieve plenty of help.

They are just like me, only you don't have to ask individually, also you need a yahoo account, if you already have one, then you are all set. If you don't, then don't worry, its a free service.