Form the AB side of the triangle, according to data of the trigonometry problem. Use the straight side of the protractor to draw the right distance or, if the side is too long, use a ruler.
Place the protractor on the left end of the AB side (vertex A). The middle point of its base (easily distinguishable on all protractors) must be directly on the vertex, and its base line (pointing at 0 and 180 degrees) must cover the AB side of the triangle.
Spot the angle the trigonometry problem gives you on the curved part of the protractor. Start from the side covering the AB part of the triangle and continue upwards. Place a dot with your pencil over the angle's spot.
Place the ruler between vertex A and the dot you just marked. Draw a line, ensuring its length is in accordance with the problem's data. The end of the new line is vertex C.
Connect vertex C and vertex B (the right end of the initial AB side) with a straight line. Use the protractor to measure the newly formed angles and verify the accuracy of your design.