SOLUTION: 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

Algebra ->  Pythagorean-theorem -> SOLUTION: 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      Log On


   

Question 72569: 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.
Answer:
Show work in this space.

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
If you scale a piece of graph paper so in the y direction it goes up at least 35 km and in
the x-direction it goes out at least 65 km, the you can make a sketch of this problem.
.
Put your pencil on the origin and draw a line up 35 km. From this point go to the right 65 km.
Then draw a line from the origin to the right end of the 65 km line. You should see that
you have drawn a right triangle with the two legs of 35 km and 65 km and the hypotenuse
being the line from the origin to the right end of the 65 km line. This hypotenuse is what you
need to find because it is the distance from the starting point to the end of your trip.
.
Recall the Pythagorean theorem that says in a right triangle the sum of the squares of the
two legs equals the square of the hypotenuse.
.
a%5E2+%2B+b%5E2+=+H%5E2
.
We can say that a = 35 km, b = 65 km and H is the distance we are trying to find.
Substitute 35 for a and 65 for b to get:
.
%2835%29%5E2+%2B+%2865%29%5E2+=+H%5E2
Now it's just calculator work. 35 squared is 1225 and 65 squared is 4225. Add these two
together and you get 5450. Substitute this into the equation for a%5E2+%2B+b%5E2 and
you get:
.
5450+=+H%5E2
.
Now all you have to do is take the square root of both sides to find that H, the distance you
have to find, is the square root of 5450. The answer is 73.82 km which rounds in the
tenths place to 73.8 km.
.
After the trip north followed by the trip east you are 73.8 miles as the crow flies from
the starting point.
.
Hope this helps you see the basics of finding distances between points on a graphed problem.