jonathans soccer team

Jonathan needs to figure out the distance between the soccer ball and himself.
Jonathan knows that with the balls height in the air and the angle between him and the ball, he can find the distance to the ball (horizontally). The ball is 10 feet high, and his line of sight to the soccer ball is 51°'s. If he uses (10/tan51), then the soccer ball will be 12.3ft away from him.
Jonathan ended up getting hit in the head with the ball since he was working out how far the ball was. The referee called timeout for Jonathan's injury and so he just watched the rest of the game on the stands.
Jonathan noticed that from a side view, the soccer goal looks like a right triangle. If he wanted to find the angle of elevation for the goal using inverse tangent, he would need to know this new triangles long & short leg. Since the soccer goal is 8 feet tall and 3 feet wide, Jonathan can make the equation tan^-1(3/8)=20.1 degrees.
After the game, Jonathan was walking home and started to notice more of how there are triangles in nature. He saw them in the flowers, the plants, pretty much everywhere.
If you look at tree's like triangles, then you can find the diagonal length of the tree between the base and the peak (the hypotenuse) using cosine. All you need is the tree's height and the angle the peak forms in relation to the bottom of the tree. If the tree is 9 feet tall, and angle the triangle/tree makes is 21 degrees, then the diagonal length of the base to the top is 9.6 feet with cos(21)=9/x.

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