Final answer:
To determine the length of the shorter base of an isosceles trapezoid, one can use trigonometry by dividing the trapezoid into simpler shapes, such as right triangles and a rectangle, and applying trigonometric functions.
Step-by-step explanation:
The student is asking for the length of the shorter base of an isosceles trapezoid given certain measures. To find this, we can employ the law of cosines or construct right triangles using the given lengths and angles and then use trigonometric functions to solve for the unknown sides.
You would start by dividing the trapezoid into two right triangles and a rectangle by drawing a line from the top vertex to the longer base perpendicular to it. Then use trigonometric functions such as cosine to find the length of the segment adjacent to the acute angle, which is common to both the rectangle part and one of the triangles. With that segment known, subtract it twice (once for each side) from the longer base's length to obtain the length of the shorter base.