A balloon is released and flies straight up for 4 miles, and then the wind blows it west for 4 miles. Find the distance between the balloon and the site where it was released.
This sounds like a right angle triangle with the distance being the hypotenuse.
Use the Pythagorean Theorem.
To find the distance between the balloon and the site where it was released, we can use the Pythagorean theorem.
Let's assume the site where the balloon was released as point A, and the final position of the balloon as point B. The vertical distance traveled by the balloon is 4 miles, and the horizontal distance traveled is 4 miles.
Using the Pythagorean theorem, the distance between points A and B can be calculated as:
Distance AB = √(vertical distance^2 + horizontal distance^2)
Substituting the given values, we have:
Distance AB = √(4^2 + 4^2)
= √(16 + 16)
= √32
≈ 5.657 miles
Therefore, the distance between the balloon and the site where it was released is approximately 5.657 miles.
To find the distance between the balloon and the site where it was released, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the balloon's movement forms a right triangle with the vertical distance it traveled (4 miles straight up) as one side and the horizontal distance it traveled (4 miles west) as the other side. The distance we're trying to find is the hypotenuse.
Using the Pythagorean theorem, we can calculate the distance:
Distance^2 = (Vertical distance)^2 + (Horizontal distance)^2
Distance^2 = (4 miles)^2 + (4 miles)^2
Distance^2 = 16 miles^2 + 16 miles^2
Distance^2 = 256 miles^2
Taking the square root of both sides:
Distance = √(256 miles^2)
Distance = 16 miles
Therefore, the distance between the balloon and the site where it was released is 16 miles.