Question

Two soccer players are warming up by kicking soccer balls at a goalie. The two players are located 10 yards apart, and the angle from each player to the goalie is 65° and 74°, respectively. What is the distance from the farthest soccer player to the goalie? 62.106 yards 14.652 yards 13.814 yards 10.606 yards

Answer 1

14

Step-by-step explanation:

Answer 2

Step-by-step 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

`\begin{gathered} \text{tan 74}\degree\text{= }(h)/(y) \\ y\text{ (tan 74}\degree)\text{= h (equation 1)} \\ y\text{ = }\frac{h}{\tan\text{ 74}\degree} \end{gathered}`

for triangle with angle 65°:

tan 65° = aopposite/adjacent

adjacent = y + 10

`\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}`
`\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}`
`\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}`