Question 73085
<pre>
Suppose you travel North for 35 kilometers, then travel East 65 kilometers. How far are you from your starting point? North and East can be considered the directions of the y and x axis respectively. Round to the tenth's place.

What is asked in the problem?
     How far are you from the starting point?

Given. 
You travel north for 35 kilometers
Then travel east 65 kilometers.


Illustration
                           Travel 65 km East
                             (Leg)
                           _____
                          |    /
                          |   /
    Tavel 35 km north     |  / <- this is the distance from the starting point
          (Leg)           | /        (Hypotenuse)
                          |/
                          .   starting point


  Notice that you form a right triangle. we use pythagorean thereom

Pythagorean Theorem states tht in a right triangle, the square of the length
of the hypotenuse is equal to the sum of the squares of the lengths of the legs

See illustration above.
     
Representation
    Let c = the Hypotenuse 
        a = the leg (north) = 35km
        b = the leg (east)  = 65 

       c^2 = a^2 + b^2
       c^2 = 35^2 + 65^2
       c^2 = 1225 + 4225
       c^2 = 5450            extract the sqrt both sides to find c.
  sqrt c^2 = sqrt 5450
         c = 73.8 km   <-------your distance from the starting point