A long-distance runner runs 3 miles south and then 7 miles east. How far is the runner from the starting point
A) 8.616 mi
B) 10 mi
C) 7.616 mi
D) 4.472 mi
I think it is eaither A or C but not sure
simple case of using Pythagoras
d^2 = 3^2 + 7^2
d^2 = 58
d = √58 = 7.616
Using the Pythagorean Theorem, I found the distance to be 7.616 miles.
a^2 + b^2 = c^2
3^2 + 7^2 = c^2
9 + 49 = 58
square root of 58 = 7.616
http://www.arcytech.org/java/pythagoras/history.html
Well, the good news is that the runner isn't lost in some endless maze! But let's figure this out. The distance from the starting point to the ending point can be found using the Pythagorean theorem. So, we have a right-angled triangle with the 3-mile and 7-mile sides.
If you remember your high school math (or you're a geometry nerd like me!), you know that the hypotenuse of this triangle represents the distance between the two points. Using the Pythagorean theorem, we can find the length of the hypotenuse.
By squaring the lengths of the sides (3^2 + 7^2), we get 58. Taking the square root of 58 gives us approximately 7.616.
So, the runner is approximately 7.616 miles from the starting point. Option C is the correct answer. And just like that, our long-distance runner can start their journey back!
To find the distance the runner is from the starting point after running 3 miles south and then 7 miles east, we can use the Pythagorean theorem.
The Pythagorean theorem states that the square of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the other two sides. In this case, the runner's distance from the starting point forms a right triangle.
The first side of the triangle is the distance traveled south, which is 3 miles.
The second side of the triangle is the distance traveled east, which is 7 miles.
To find the hypotenuse (distance from the starting point), we can use the formula:
hypotenuse equals the square root of (3^2 + 7^2).
Calculating this, we get:
hypotenuse equals the square root of (9 + 49).
hypotenuse equals the square root of 58.
hypotenuse is approximately 7.616 miles.
Therefore, the correct answer is C) 7.616 miles.