A traveler went 10 miles south, 7 miles east, 2 miles south, and 2 miles west. How many miles is the traveler from the start?
He's 12 miles south of the start and 5 miles east of the start.
This makes a right angle triangle. You can find the closest distance by finding the hypotenuse of this triangle by using the Pythagorean Theorem.
12^2 + 5^2 = h^2
144 + 25 = h^2
169 = h^2
13 = h
Thanks Ms.Sue.... you're awesome!
You're welcome -- whoever you are.
But please keep the same name for your posts.
To find out how many miles the traveler is from the start, we need to calculate the net displacement of the traveler from the starting point.
Let's break down the given directions step by step:
1. The traveler went 10 miles south.
This means the traveler moved 10 miles in the opposite direction of the North. As we are calculating displacement, we consider south as a negative direction. So, the displacement for this step is -10 miles.
2. The traveler then went 7 miles east.
Moving east simply means moving in the positive direction of the x-axis. So, the displacement for this step is +7 miles.
3. The traveler went 2 miles south.
Similar to the first step, moving south is considered a negative direction. So, the displacement for this step is -2 miles.
4. Finally, the traveler went 2 miles west.
Moving west means moving in the negative direction of the y-axis. So, the displacement for this step is -2 miles.
Now, we can calculate the net displacement by adding up all the displacements:
-10 miles + 7 miles + (-2 miles) + (-2 miles)
Simplifying this expression, we get:
-10 + 7 - 2 - 2 = -5 miles
Therefore, the traveler is 5 miles away from the starting point.