Elena jogs 7 kilometers west and then 5 kilometers down south. She stops and checks her time. How far is she from her starting point?
This looks like a problem for Pythagoras.
a^2 + b^2 = c^2
7^2 + 5^2 = c^2
49 + 25 = c^2
74 = c^2
8.6 km = c
To find out how far Elena is from her starting point, we can use the concept of a "right triangle" formed by her jogging routes. Elena jogs 7 kilometers west and 5 kilometers south, so her jogging routes create two sides of a right triangle.
To calculate the distance Elena is from her starting point, we can calculate the length of the hypotenuse of this right triangle using the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b) in a right triangle.
In this case, the two sides are 7 kilometers (west) and 5 kilometers (south). Let's use "a" to represent 7 kilometers and "b" to represent 5 kilometers.
According to the Pythagorean theorem, we have:
c^2 = a^2 + b^2
Replacing the variables with the given values:
c^2 = 7^2 + 5^2
Simplifying:
c^2 = 49 + 25
c^2 = 74
To find the value of "c" (the distance Elena is from her starting point), we need to take the square root of 74:
c = √74
Using a calculator, we can find that the square root of 74 is approximately 8.602.
Therefore, Elena is approximately 8.602 kilometers away from her starting point.