on a softball field, home plate is 43 feet from the pitchers mound. a ball is hit at an angle of 27° east of…
on a softball field, home plate is 43 feet from the pitchers mound. a ball is hit at an angle of 27° east of the pitchers 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 the law of cosines formula
The law of cosines for a triangle with sides (a), (b), (c) and the angle (C) opposite to side (c) is (c^{2}=a^{2}+b^{2}-2ab\cos C). Let (a = 43), (b = 162), and (C=27^{\circ}).
Step2: Substitute values into the formula
[ \begin{align*} c^{2}&=43^{2}+162^{2}-2\times43\times162\times\cos(27^{\circ})\ c^{2}&=1849 + 26244-13932\times\cos(27^{\circ})\ \end{align*} ] We know that (\cos(27^{\circ})\approx0.891). [ \begin{align*} c^{2}&=1849+26244 - 13932\times0.891\ c^{2}&=1849+26244-12413.412\ c^{2}&=28093 - 12413.412\ c^{2}&=15679.588 \end{align*} ]
Step3: Solve for (c)
[c=\sqrt{15679.588}\approx125]
Answer:
125 feet