This is Dragonite. He excels at kicking field goals and aspires to be in the NFL. He plays football internationally with different size field goals, so every time he gets on the field he has to calculate the dimensions he doesn't know in order to kick a successful field goal.
This is a 40 yard field goal with the angle to the goal post being 60°, but dragonite doesn't know how high the goal post is. He does tan(60)·40=69.28. The goal post is 69.3 yards high.
Here, Dragonite knows how far away he is and how high the goal post is. He sees that its 30 yards high and he is 35 yards away, but he doesn't know the angle to the goal post from where he is. He does tan−1(30/35)=40.60. So the angle to the goal post is 40.6°.
In this game Dragonite is aware of the distance from him to the top of the goal post, as well as the angle to the post. He doesn't know the distance in yards to the bottom of the post, so he does cos(50)· 60= 38.57. He is 38.6 yards away from the bottom of the post.
Here, Dragonite knows the angle to the goal post, and how high the goal post is. He needs to find out the distance to the top of the goal post, so with the height of it being 45 yards and angle being 45°, he does (45)/(sin 45)= 63.6. He now knows the distance to the top of goal post, which is 63.6 yards.
After a long, tiring, and demanding season, Dragonite finally completed his dream of making it to the NFL. He was drafted 1st overall to the Cleveland Browns!