you walk north for 2.5 miles. Then you walk east a distance of 3 miles. How many miles from the starting point are you?
d^2 = x^2 + y^2
d^2 = 3^2 + 2.5^2
d = sqrt (9 + 6.25)
d = sqrt (15.25)
d = 3.91 miles
Well, if you walked north for 2.5 miles and then east for 3 miles, you must be completely lost! Who walks in random directions like that? But to answer your question, you would be 3.905 miles away from the starting point. Now, I hope you have someone with a GPS to help you find your way back!
To find the distance from the starting point, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the northward walk and the eastward walk form two sides of a right triangle, with the distance from the starting point being the hypotenuse.
First, let's calculate the square of the northward distance:
2.5 miles * 2.5 miles = 6.25 square miles
Next, let's calculate the square of the eastward distance:
3 miles * 3 miles = 9 square miles
Now, we can sum up the squares of these two distances:
6.25 square miles + 9 square miles = 15.25 square miles
Finally, we can find the square root of the sum to determine the distance from the starting point:
√15.25 square miles ≈ 3.9 miles
Therefore, you are approximately 3.9 miles from the starting point.
To find out how many miles you are from the starting point, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, you have walked 2.5 miles north and 3 miles east, forming a right triangle. The distance from the starting point to your new position represents the hypotenuse of this triangle.
Using the Pythagorean theorem, you can calculate the length of the hypotenuse as follows:
Hypotenuse^2 = (2.5)^2 + (3)^2
Hypotenuse^2 = 6.25 + 9
Hypotenuse^2 = 15.25
Hypotenuse ≈ 3.90 (rounded to two decimal places)
Therefore, you are approximately 3.90 miles from the starting point.