1) In this problem we need to find x, being an angle in the right triangle. To solve this missing angle, we use sine with the two side lengths we are given. (Opposite/Adjacent) Then, we move sine to the opposite side of the equation, leaving us with it’s opposite: sine-1. We multiply this with the fraction and are given the missing angle.

2) This right triangle leaves us with a missing side length of the hypotenuse. We take x, and put it in a fraction with the other side length we are given, (6/x) using cosine. We then reciprocate the fraction, OR switch the numerator on the left side with the denominator on the right side. This leaves us with only x, and the missing equation for the length on the other side.

3) In this problem we are solving for another missing side length. In this case we will use tangeant, because x is the opposite side and the OTHER length we are given is the adjacent: 10 mm. From here we use the reference angle with tangeant, and then the fraction on the other side. (x/10) Next, we take the 10, and multiply it with the other side of the equation giving us the missing side length.