Dot Product Question: Find Angle in Basketball Gym

[LeakyFrog]

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.

 

[Dick]

How about computing the dot product in a vector way as the next step?

 

[LeakyFrog]

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?

 

[Dick]

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.