(Originais Teachy 2024) - Question Hard of Mathematics

During an interdisciplinary project of Architecture and Mathematics, a group of high school students is working on the design of a stained glass window for a modernist building. The envisioned stained glass window has a radially symmetric design, and to calculate the precision of the glass cuts, it is necessary to determine the exact dimensions of each sector of the stained glass window. One of the sectors is an angular circular segment with a central angle of 75°, extending from the center of the circle to its circumference. To ensure the visual harmony of the stained glass window, the students need to calculate the exact measure of the radius of this circular sector. Considering the knowledge of trigonometric functions of the given angles and the relationship between the arc length and the radius to determine the dimensions of the circular sector, what is the exact value of the radius that the students should use to draw this sector of the stained glass window?