Question

Use the law of cosines to solve the problem.on a baseball field, the pitcher's mound is 60.5 feet from home plate. during practice, a batter hits a ball 216 feet. the path of the ball makes a 34° angle with the line connecting the pitcher and the catcher, to the right of the pitcher's mound. an outfielder catches the ball and throws it to the pitcher. how far does the outfielder throw the ball

Answer 1

Answer: 169.26 feet.

Step-by-step explanation:

Here, The distance of pitcher's mound from the home plate = 60.5 feet

And, the distance covered by ball when it was hit by the bat = 216 feet

Let the outfielder throw the ball from the distance x feet.

Thus, by the below diagram,

$x^2=216^2+60.5^2-2\times 216\times 60.5\times cos(34^{\circ})$

$x^2=46656+3660.25-21667.7259963 =28648.5240037$

$\implies x = 169.258748677\approx 169.26\text{ feet}$

Hence, the outfielder throw the ball from the distance of 169.26 feet Approximately.