Question

On a softball field, home plate is 43 feet from the pitcher’s mound. A ball is hit at an angle of 27° east of the pitcher’s mound. The ball travels 162 feet before it is caught by an outfielder. Law of cosines: a2 = b2 + c2 – 2bccos(

a. Rounded to the nearest foot, the outfielder must throw the ball feet to return it to the pitcher.

Answer 1

the answer is 125 feet

Answer 2

125 feet

Explanation:

Given :

On a softball field, home plate is 43 feet from the pitcher’s mound.

A ball is hit at an angle of 27° east of the pitcher’s mound.

The ball travels 162 feet before it is caught by an outfielder.

To Find : Rounded to the nearest foot, the outfielder must throw the ball feet to return it to the pitcher.

Solution:

Law of cosines:
`a^2 = b^2 + c^2 -2bc cos A`

∠A = 27°

b = 43

c = 162

Substitute the given values

`a^2 = 43^2 + 162^2 -2(43)(162) cos 27^(\circ)`

`a^2 = 15679.497105`

`a = √(15679.497105)`

`a =125.21`

The outfielder must throw the ball 125 feet to return it to the pitcher.