Problema Solution
A basketball gymnasium is 35 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 at the top of the wall behind one basket to the diagonally opposite corners of the gym floor. What is the cosine of the angle θ made by the strings as they cross?
Answer provided by our tutors
Let:
u= (0, 200, 0)-(0,0,35)=(0,200,-35)
v=(80,0,0)-(0,0,35)=(80,0,-35)
Cos x = (u*v)/[|u||v|]
u*v=(0,200,-35)*(80,0,-35)=0(80)+200(0)+(-35)(-35)=0+0+1225=1225
|u|=sqrt(0+200^2+(-35)^2)=203.04
|v|=sqrt(80^2+0+(-35)^2)=87.32
Therefore:
Cosx=1225/(203.04*87.32)
x=86.04 degrees