Question

cos theta = 5/7 ,(270degree 12 years ago

Answer 1

Think about a right triangle OAB where O=(0,0) is the origin, B=(0,5), A=(5, - 2\(\sqrt 6\)) and \(\theta = 2 \pi - AOB)\) then
\[
\sin(\theta) =- \frac {2\sqrt 6}{7}

\]
Since you have sin and cos you can find the rest.

Answer 2

Notice that
\[
OA^2 = (2 \sqrt 6)^2 + 5^2 = 49 \\
OA=7

\]

Answer 3

As always, practice trig on my site
http://www.math.missouri.edu/escgi/mucgi-bin/munew.cgi?variable=trig