The Pythagorean Theorem and Its Converse Problem Set

It is the first week of football season, and you are eagerly awaiting the 1:00 p.m. start time for your favorite team. Your teacher has asked you to watch the game as part of your upcoming homework assignment. You wonder what your math studies have to do with football.

The next day as you enter class, you find following assignment posted on the board. Answer the following questions:

1. Player A throws the ball 25 yards to Player B. After catching the ball, Player B immediately turns 90 degrees to his left and runs with the ball for 30 yards. At the end of the play, how far away is the ball from where it started? Round your answer to the nearest whole number.
   
   
2. Player A catches the ball and throws it 4 yards to Player B. Then, Player B turns and throws the ball 8 yards to Player C, who is standing in the end zone 10 yards from Player A. Given the players' positions when they caught the ball, do the players form a right triangle?
   
   
3. Player A kicks the ball 70 yards down the field away from the end zone. Player B catches the ball and runs 40 yards toward the end zone at an angle. At the end of the play, how far apart are Player A and Player B if the resulting triangle is a right triangle? You may round your answer to the nearest whole number.

This activity is also available in a printable document.

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