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

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

Explanation:

It is given that 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.

Now, applying the law of cosines,

`a^2=b^2+c^2-2bccosA`,

Putting b=43, c=162 and A=27°, we have

`a^2=(43)^2+(162)^2-2(43)(162)cos27^(\circ)`

`a^2=1849+26244-12413.4`

`a^2=15679.6`

`a=125.21`

`a`≈
`125 feet`

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