This is Gengar! Gengar is a high school soccer player and wants to be a professional player one day! Therefore, Gengar must practice his accuracy and technique in shooting the ball. So, Gengar set himself up for a challenge to hit the crossbar of a goal. He will attempt to do this from various distances, heights, and styles. Do you think Gengar is up for the challenge? Let's find out!
By: Rohan Kapadia
Gengar attempts to hit the crossbar of this goal which is 10 feet tall. The angle of elevation form the ball to the crossbar is 32 degrees. He decides to find x and y in order to use the Pythagorean Theorem. He does 10 divided by sin(32). He got 18.9 feet as the x side. He was then able to do y^2 + 10^2 = 357.2. 357.2-100=257.2. So square root of 257.2 is about 16 feet(y side)
Gengar is on top of a mountain of boxes trying to hit the crossbar from 5 feet higher than the height of the goal. The angle of depression is 21 degrees. Gengar wants to know how far he is from the crossbar (x). So, he decides to do 5 divided by tan(21). He got about 13 feet as the x value.(distance from Gengar to crossbar)
Gengar decides to take a run up to the ball and kick with a distance of 6ft from the goal. The goal is 10ft tall. Gengar wants to find the angle of elevation in order to hit a precise shot. So, he used tan^-1 (10/6). Using this equation, Gengar found that the angle is 59 degrees.
Gengar wants to shoot at a goal of different height and from a farther distance. Gengar decides to shoot a longer ball from 30ft away from the goal. Using the 47 degree angle of elevation, Gengar wants to know the height of the goal. He does tan(47) times 30. Gengar finds that the height of the new goal is about 32ft tall.
THE CROSSBAR CHALLENGE
Thank you for joining Gengar in his Crossbar Challenge journey! I hope you enjoyed all of Gengar's shots and tricks which required skill and knowledge in math! Although Gengar's challenge was very difficult, he was able to overcome it with his Trigonometric skills he had learned! As you can see, Trigonometry can be successfully used wherever you are!