On a baseball field, the pitcher's mound is 60.5 feet from home plate. During practice, a batter hits a ball 214 feet at an angle of 36° to the right of the pitcher's mound. An outfielder catches the ball and throws it to the pitcher. Approximately
how far does the outfielder throw the ball?

9514 1404 393

  169 ft

Step-by-step explanation:

The law of cosines can be used to find the distance from the outfielder to the pitcher. It tells you for triangle ABC, the length of side c can be found from ...

  c² = a² +b² -2ab·cos(C)

Here, we hve a=60.5, b=214, and C=36°. Then the desired distance is ...

  c = √(60.5² +214² -2·60.5·214·cos(36°)) ≈ √28507.56 ≈ 168.84

The outfielder throws the ball about 169 feet.