Explanation:
To answer the question, we need an illustration to make it easier:
We will solve for the unknown:
let the distance from player1 to goalie = y
The distance from farthest soccer player to goalie is the distance from the player 2 to goalie
from the diagram, the distance from the player 2 to goalie = y + 10 yrads
the distance from the player 2 to goalie = y + 10
for the triangle with angle 74°:
To determine y, we will use tan ratio (TOA)
tan 74° = opposite/adjacent
[tex]\begin{gathered} \text{tan 74}\degree\text{= }\frac{h}{y} \\ y\text{ (tan 74}\degree)\text{= h (equation 1)} \\ y\text{ = }\frac{h}{\tan\text{ 74}\degree} \end{gathered}[/tex]for triangle with angle 65°:
tan 65° = aopposite/adjacent
adjacent = y + 10
[tex]\begin{gathered} \tan \text{ 65}\degree\text{ = }\frac{h}{y\text{ + 10}} \\ (y\text{ + 10)(tan65}\degree)\text{ = h (equation 2)} \\ \\ The\text{ function of h we got above is h = y(tan 74}\degree) \\ \text{equating both equations}\colon \\ h\text{ = h} \\ (y\text{ + 10)(tan65}\degree)\text{ = }y\text{ (tan 74}\degree) \\ (y\text{ + 10)(2.}1445)\text{ = y(3.4874)} \\ 2.1445y\text{ + 21.445 = 3.4874y} \\ 21.445\text{ = 3.4874y - }2.1445y \end{gathered}[/tex][tex]\begin{gathered} 21.445\text{ = 1.3429y} \\ \text{divide both sides by 1.3429:} \\ \frac{21.445\text{ }}{1.3429}\text{ = y} \\ y\text{ = 15.97} \end{gathered}[/tex][tex]\begin{gathered} \text{distance from the 2nd player to goalie = 15.97 + 10 } \\ \text{distance from the 2nd player to goalie }=\text{ 25.97} \end{gathered}[/tex]
