To find the degree measure of the angle facing the longer leg in a right triangle, you can use the inverse tangent function.
where θ is the angle measure, "opposite" is the length of the leg opposite the angle, and "adjacent" is the length of the leg adjacent to the acute angle.
In this case, the longer leg (13 inches) is opposite the angle we're interested in, and the shorter leg (7 inches) is adjacent to the angle.
Using a calculator, the arctan of 7/13 is approximately 29.74 degrees. Therefore, the degree measure of the angle facing the longer leg is approximately 29.74 degrees.