Take 10:2 and multiply each number by another number (to get the unsimplified answer). This would turn it into 10x:2x. Then you add the two terms together to get 12x = 60. Divide both sides by 12 to get the x by itself, and you'll get x = 5. Now, if you go back to the original 10x:2x equation and substitute x for 5 [10(5):2(5)], you'll get 50:10, which is 50 students to 10 teachers.
In degree mode, the answer is around 83. You use the inverse tangent button on the calculator to get rid of the tangent and find what theta is (make sure your calculator is in degree mode)