Question

In a basketball drill, two players start at the same spot on the court. One player runs 6 feet

down the court and the other player runs 4.5 feet across the court (in a direction perpendicular
to the first player). What is the distance that one player must pass the ball for it to reach the
other?

Answer 1

`\boxed{\text{7.5 ft}}`

Explanation:

If the players are running perpendicular to each other, we have a right triangle, as in the diagram below.

We can apply Pythagoras' Theorem.

`\begin{array}{rcl}a^(2) & = & b^(2) + c^(2)\\& = & 4.5^(2) + 6^(2)\\& = & 20.25 +36\\& = & 56.25\\a & = & √(56.25)\\& = & \mathbf{7.5}\\\end{array}\\\text{The distance between the two players will be } \boxed{\textbf{7.5 ft}}`

Answer 2

7.5 ft

Explanation:

The distance can be found using the Pythagorean theorem. The given distances form the legs of a right triangle, and the ending distance (d) between the players is its hypotenuse. The Pythagorean theorem tells you ...

d² = (6 ft)² +(4.5 ft)² = 36 ft² +20.25 ft²

d² = 56.25 ft² = (7.5 ft)² . . simplifying and rewriting as a square

d = 7.5 ft . . . . . . . . . . . . . . . taking the positive square root

The ball must be passed a distance of 7.5 ft for it to reach between players.

_____

If you recognize the given numbers as having the ratio 3:4, then you may realize they are the legs of a 3-4-5 right triangle with a scale factor of 1.5. The distance between players will be 1.5×5 = 7.5 feet.