CPhill

Ok....we know an angle, an adjacent side, and we're trying to find the opposite side.....so....the tangent function seems to be what we need...so we have....

tan (24) = opp/ 16.9     multiply both sides by 16.9

16.9 tan (24) = about 7.5 cm

Here's my contribution to this ....

The total arrangements for any 7 people sitting in a row is 7!  = 5040

We can seat the 3 people together in five different ways.....(seats 1 - 5)

And for each of these there are 3! ways they can be arranged

So, the total number of ways they can sit together is:

(5 * 3!) = 30

So....the probability that they don't sit together is

1 - ( the probability they do sit together) =

1 - 30/5040  = 0.994047619047619    = about 99%

I don't know if this is correct......if anuone spots a flaw in my logic.....I'll be glad to know!!!

OK....that's a horse of a different color.....!!!

So we have

cos^-1 (((3*sqrt(3)+4) /(5*sqrt(10)))   =  54.43573387782 degrees

And there you go.....!!!

Just subtract 3 from the "x value" of each coordinate and add 4 to each "y" value.....

It's an old joke between us, happy7......Melody and I are known to give some very "creative" answers to probability questions........some of them even turn out to be correct.....!!!!

Yep......out of our minds !!!! LOL!!!

The cosine of anything can't be equal to 54 !!!

I just evaluated what the questioner asked......in fact....I "pasted" it directly into the onsite calculator....!!!

Thanks......hey .....we actually agree on 2 probabilty problems......what's the probability ???

I believe the probability of 13 is:

6 6 1   3 ways to do this

6 5 2   6 ways to do this

6 4 3   6 ways to do this

5 5 3   3 ways to do this

5 4 4   3 ways to do this   =       

21 total ways to roll a 13

So....the probability is

21 / 216  = 0.0972222222222222  = about 10%

The expression in the parentheses evaluates to about 0.58161574731657

If this is degree measure, we have

cos(0.58161574731657) = about .9990  (almost 1, since this is close to 0 degrees)

If this is radian measure, we have

cos(0.58161574731657) = about .836