Three baseball players are playing catch. Barry is 12 feet south of Regan and 16 feet west of Addison. How far does Regan need to throw the ball to get it to Addison?
To find the distance Regan needs to throw the ball to get it to Addison, we can use the Pythagorean theorem.
Let's assume that Barry is at point B, Regan is at point R, and Addison is at point A.
Since Barry is 12 feet south of Regan, we can draw a vertical line connecting B and R with a length of 12 feet.
Since Barry is 16 feet west of Addison, we can draw a horizontal line connecting B and A with a length of 16 feet.
This creates a right-angled triangle with one side measuring 12 feet and the other side measuring 16 feet.
To find the length of the hypotenuse, which is the distance Regan needs to throw the ball to get it to Addison, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):
c^2 = a^2 + b^2
Let's substitute the values into the equation:
c^2 = 12^2 + 16^2
c^2 = 144 + 256
c^2 = 400
To find the value of c, we need to take the square root of 400:
c = sqrt(400)
c = 20
Therefore, Regan needs to throw the ball a distance of 20 feet to get it to Addison.
To find how far Regan needs to throw the ball to get it to Addison, 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, we can consider the distance between Barry and Addison as the hypotenuse of a right triangle, with the distances between Barry and Regan, and Regan and Addison as the other two sides.
Let's denote the distance between Barry and Regan as x and the distance between Regan and Addison as y.
According to the problem, x = 12 feet and y = 16 feet.
To find the length of the hypotenuse (distance between Barry and Addison), we can use the Pythagorean theorem:
\(x^2 + y^2 = c^2\)
Plugging in the given values:
\(12^2 + 16^2 = c^2\)
\(144 + 256 = c^2\)
\(400 = c^2\)
Taking the square root of both sides:
\(c = \sqrt{400}\)
\(c = 20\)
Therefore, Regan needs to throw the ball a distance of 20 feet to reach Addison.
To determine how far Regan needs to throw the ball to get it to Addison, 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 scenario, we have a right triangle with one side measuring 12 feet (south) and the other measuring 16 feet (west). Let's assume this right triangle is formed by drawing a line connecting Regan and Addison. The distance that Regan needs to throw the ball is the length of the hypotenuse.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse (c) as follows:
c^2 = a^2 + b^2
where c is the hypotenuse, and a and b are the lengths of the other two sides of the triangle.
Plugging in the values we know:
c^2 = 12^2 + 16^2
c^2 = 144 + 256
c^2 = 400
Taking the square root of both sides of the equation:
c = √400
c = 20
Therefore, Regan needs to throw the ball a distance of 20 feet to get it to Addison.