on a softball field, home plate is 43 feet from the pitcher’s mound. a ball is hit at an angle of 27° east…

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. how far must the outfielder throw the ball to return it to the pitcher? round to the nearest foot. 112 feet 125 feet 145 feet 156 feet

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. how far must the outfielder throw the ball to return it to the pitcher? round to the nearest foot. 112 feet 125 feet 145 feet 156 feet

Answer

Explanation:

Step1: Identify triangle sides/angle

We have a triangle with two sides: $a=43$ ft, $b=162$ ft, and included angle $\theta=27^\circ$. We need the third side $c$ (the throw distance). Use the Law of Cosines: $$c^2 = a^2 + b^2 - 2ab\cos\theta$$

Step2: Substitute values into formula

$$c^2 = 43^2 + 162^2 - 2(43)(162)\cos(27^\circ)$$ Calculate each term: $43^2=1849$, $162^2=26244$, $2(43)(162)=13812$, $\cos(27^\circ)\approx0.8910$ $$c^2 = 1849 + 26244 - 13812(0.8910)$$

Step3: Compute intermediate results

$$1849+26244=28093$$ $$13812(0.8910)\approx12306.49$$ $$c^2 \approx 28093 - 12306.49 = 15786.51$$

Step4: Solve for c

$$c = \sqrt{15786.51} \approx 125.64$$ Round to nearest foot: $c\approx126$, closest to 125 ft.

Answer:

B. 125 feet