The document uses the Pythagorean theorem to find the hypotenuse of a right triangle given sides a=10 and b=17.3, calculating the hypotenuse c to be 19.98. It then uses tangent to find the measure of angle B as 59.97 degrees. Finally, it uses the fact that interior angles of a triangle sum to 180 degrees to solve for the unknown angle A of 30.03 degrees.