if i have a right triangle how do i solve for one of the angles when i am giving the opposite and the adjacent to it?
\(\tan(\text{ the angle }) = \frac{ (\text{ length of side opposite the angle })}{(\text{ length of side adjacent the angle })}\)
Just plug in the information that you have and solve for whatever you need.
The reverse of tan is arctan. (This can also be expressed as atan or tan-1.)
\(( \text{ the angle }) = \arctan(\frac{ (\text{ length of side opposite the angle })}{(\text{ length of side adjacent the angle })})\)
The reverse of sin is arcsin (or asin or sin-1).
The reverse of cos is arccos (or acos or cos-1).
Another thing to remember is that the adjacent side can never be the hypotenuse.