Answer: The player will not score the goal, since the height of the puck is 4.3 ft, which is greater than the height of the goal (4 ft)
Step-by-step explanation:
If we model this situation as a right triangle, in which the angle is [tex]\theta=7\°[/tex], the opposite leg to that angle is the height [tex]h[/tex] of the puck and the adjacent leg is the distance between the player and the goal line ([tex]35 ft[/tex]); we can use the tangent trigonometric function to find the height:
[tex]tan \theta=\frac{opposite-leg}{adjacent-leg}[/tex]
[tex]tan(7\°)=\frac{h}{35 ft}[/tex]
Isolating [tex]h[/tex]:
[tex]h=tan(7\°)(35 ft)[/tex]
[tex]h=4.29 ft \approx 4.3 ft[/tex]
If we compare this height with the height of the goal (4 ft) we will find out that the player will not be able to score the goal, since the height of the puck is greater than the height of the goal.
