You will use SOHCAHTOA and a trigonometry chart.
SOHCAHTOA is an acronym used to represent the equations of sine, cosine, and tangent.
Let's say you had this triangle with an angle
Sine: measure of the opposite leg divided by the measure of the hypotenuse.
Cosine: measure of the adjacent(touching) leg divided by the measure of the hypotenuse.
Tangent: measure of the opposite leg divided by the measure of the adjacent leg.
This website provided helpful examples and explanations as well:(http://www.mathwords.com/s/sohcahtoa.htm)
Your teacher will most likely also provide you with a trigonometry chart. It is very unlikely any teacher will expect a student to memorize it. To use the chart you will find sine, cosine, or tangent column along the top and follow the column down to the closest value to your answer you found using SOHCAHTOA. Next to this value on the chart there will be a degree which is your answer.