Dot Product Question: Find Angle in Basketball Gym

In summary, to find the cosine of the angle made by two strings crossing in a basketball gymnasium, you can first interpret the strings as vectors and calculate their dot product. Then, divide the dot product by the magnitude of the vectors and use the inverse cosine to find the angle. In this case, the angle is approximately 43.30 degrees.
  • #1
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Homework Statement


A basketball gymnasium is 25 meters high, 80 meters wide, and 200 meters long. For a half time stunt , the cheerleaders want to run two strings, one from each of the two corners above one basket to the diagonally opposite corners of the gym floor. What is the cosine of the angle made by the strings as they cross?

Homework Equations



||A||||B||cos(theta)

The Attempt at a Solution



So far I have interpreted the two strings as the vectors:
P1 = -80i + 200j + 25k
P2 = 80i +200j +25k

The magnitude of both the strings is √47025m2 ≈ 216.85m.

I'm just not sure the next step to take.
 
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  • #2
How about computing the dot product in a vector way as the next step?
 
  • #3
So after taking the dot product of the two vectors I got

P1.P2 = -80m*80m + 200m*200m + 25m*25m = 34225m2

then I took that and divided it by the magnitude of the vectors

cos(theta) = 34225m2/216.85m2

used inverse cosine and found

theta = 43.30 degrees.

Does that method all sound about right?
 
  • #4
LeakyFrog said:
So after taking the dot product of the two vectors I got

P1.P2 = -80m*80m + 200m*200m + 25m*25m = 34225m2

then I took that and divided it by the magnitude of the vectors

cos(theta) = 34225m2/216.85m2

used inverse cosine and found

theta = 43.30 degrees.

Does that method all sound about right?

That sounds great.
 

1. What is the dot product in basketball?

The dot product in basketball is a mathematical calculation used to determine the angle between two vectors on a basketball court. It is used to analyze the accuracy and precision of shots taken by players.

2. How is the dot product calculated in basketball?

The dot product is calculated by multiplying the magnitude (length) of two vectors and the cosine of the angle between them. In basketball, the vectors represent the direction and distance of the ball's trajectory and the target (e.g. hoop or backboard).

3. What does the angle in the dot product represent in basketball?

The angle in the dot product represents the deviation from a straight line between the shooter and the target. A smaller angle indicates a more accurate shot, while a larger angle indicates a less accurate shot.

4. How is the dot product used in basketball analysis?

The dot product is used in basketball analysis to evaluate the shooting performance of players. By calculating the dot product for each shot, analysts can identify trends in accuracy and determine areas for improvement.

5. Can the dot product be used to improve shooting in basketball?

Yes, the dot product can be used to improve shooting in basketball by identifying and correcting any inconsistencies or errors in a player's shooting technique. By understanding the angle of their shots, players can make adjustments to improve their accuracy.

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