1. Draw a sketch! (see attachment)

2. You are dealing with 2 different right triangles. Use the 1st one to determine the necessary interior angles. (The midpoint of the curve is located on the angle bisector of the angle of 155°)

3. Use the indicated grey right triangle to calculate the length of R:

Solve for R.

EDIT: I've made a typo: Instead of 72.5° it should read 77.5°