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February 2nd, 2015, 08:59 PM   #1
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Finding the cosine angle

So my problem is
A basketball gymnasium is 40 meters high, 80 meters wide and 170 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?


So my work is
taking the magnitude of both the equations
(80i+170j+40k) and (-80i+170j+40k) which is 192.094

so then I would take that, and divide it by the dot product of my two vectors and take the arccos of that,

the dot product I got was ... 24100.

so arccos(192.094/24100)

my calculator is telling me undef, I don't know where I am going wrong...
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February 3rd, 2015, 06:30 AM   #2
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I don't think you need to take arccos. After all, the question is not asking for the angle; only the cosine of the angle.

Also, $\displaystyle \cos \theta = \frac{u\cdot v} {|u||v|}$

If you wanted to find the angle, you would have $\displaystyle\cos \theta = \frac{24100} {192.094^2}$

Last edited by neelmodi; February 3rd, 2015 at 06:34 AM.
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