Question

On a baseball field, the pitcher’s mound is 60.5 feet from home plate. During practice, a batter hits a ball 195 feet at an angle of 32° 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?

Answer 1

The problem is modelled in the diagram below

We will use the cosine rule to find x

x² = 60.5² + 195² - [2×60.5×195×cos(32°)]
x² = 3660.25 + 38025 - [23595 × cos(32)]
x² = 41685.25 - 19683.50019
x² = 22001.74981
x = √22001.74981
x = 148.33 feet (rounded to 2 decimal place)

Note: the cosine rule is shown in the second diagram below