A car traveled 48 miles west and then 14 miles south. How far is the
car from its starting point? _____
you are finding the length of the hypotenuse ...
h^2 = 48^2 + 14^2
....
To find the distance between the car's starting point and its current position after traveling 48 miles west and then 14 miles south, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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, the distances traveled west and south form the legs of a right-angled triangle, and the distance we're looking for is the hypotenuse.
To find the distance, we can follow these steps:
1. Determine the squares of the distances traveled west and south.
- The distance traveled west is 48 miles, so its square is 48^2 = 2304.
- The distance traveled south is 14 miles, so its square is 14^2 = 196.
2. Add the squares of the distances together: 2304 + 196 = 2500.
3. Take the square root of the sum to find the distance:
- The square root of 2500 is 50.
Therefore, the car is 50 miles away from its starting point.
To find out how far the car is from its starting point, we can use the Pythagorean theorem. The Pythagorean theorem 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 car's path forms a right triangle.
We can consider the distance traveled west as one side, the distance traveled south as the other side, and the distance from the starting point to the car's current position as the hypotenuse. Using this information, we can find the distance using the formula:
c^2 = a^2 + b^2
where c represents the hypotenuse and a and b represent the other two sides.
Let's calculate the distance using this formula:
1. Square the distance traveled west: 48^2 = 2304.
2. Square the distance traveled south: 14^2 = 196.
3. Add the two squared distances together: 2304 + 196 = 2500.
4. Take the square root of the sum to get the distance from the starting point: √2500 = 50.
Therefore, the car is 50 miles from its starting point.