For each of these problems, remember SOH-CAH-TOA.
Sine = opposite/hypotenuse
Cosine = adjacent/hypotenuse
Tangent = opposite/adjacent
5) Here we are looking for the cosine of the 30 degree angle. Cosine uses the adjacent side to the angle over the hypotenuse. Therefore, cos(30) = 43/50.
6) We have an unknown side length, of which is adjacent to 22 degrees, and the length of the hypotenuse. Since we know the adjacent side and the hypotenuse, we should use Cosine. Therefore, our equation to find the missing side length is cos(22) = x / 15.
7) When finding an angle, we always use the inverse of the trigonometry function we originally used. Therefore, if sin(A) = 12/15, then the inverse of that would be sin^-1 (12/15) = A.
8) We are again using an inverse trigonometry function here. We know the hypotenuse, as well as the side adjacent to the angle. Therefore, we should use the inverse cosine function. Using the inverse cosine function gives us cos^-1 (9/13) = 46 degrees.
Hope this helps!
