math
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- "Trigonometric Soccer"by Japneet Sandhu Math 2 H
- This is Gianna. She plays soccer at MHHS. Today, she has a game and she will be showing how she uses sin, cos, and tan to score goals!
- To find the angle, we have to multiply sin-1 (opposite/hypotenuse). So, we would end up with the equation sin-1 (6/11). After calculating this, we get...
- 11 ft
- 6 ft
- The clock was ticking and the game was about to be over. Gianna's team was hopeless and thought the game would be a tie, since the score was 11-10. But, Gianna scored a goal! How far did her goal go?
- Gianna just scored a goal! What angle did she kick the ball at? Let's use sin-1 to figure out the angle.
- About 33 degrees!
- Oh no! The goalie almost blocked Gianna's shot, but she scored the goal! This kick was shorter than the last one. Let's find out how many feet Gianna kicked the ball.
- To find the distance of the kick (hypotenuse), we have to do cos(60) = 4/x. Then, we cross-multiply. With this, we get cos(60)x = 4. To cancel out the x, we will do 4/cos(60). The distance of the kick is...
- 8 feet!
- 4 ft.
- ?
- 60o
- To find the distance of the goalie's shot, we have to do tan(54) = 7/x. After, we cross-multiply and are left with tan(54)x = 7. Now, to cancel out the x, we have to do 7/tan(54). The distance of the goalie's shot is...
- 54o
- ?
- 7 feet
- No! The goalie kicked Gianna's shot! How far did the goalie's shot go? Let's see.
- About 5 feet!
- In order to find the distance of her winning goal, we must do sin(45) = x/10. Then, we cross-multiply and get 7.07 = x. So, the distance is...
- 10 ft.
- 45o
- ?
- About 7 feet!
- thank you for supporting Gianna and her soccer game!
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