Question

A company builds metal stands for bicycle wheels. a new design calls for a v-shaped stand that will hold wheels with a 13-inch radius. the sides of the stand form a 70° angle to the nearest tenth of an inch, what should the length of the side of the v-shaped stand be so that it is tangent to the wheel?

Answer 1

The length of the side = The length of the arc intercepted by the central
angle

∴ length = Θ r
where Θ = central angle in radians
and     r  = radius

∴  Θ = 70° = 70 * π /180
     r  = 13 in.

∴ length = (70 * π /180) * 13 ≈ 15.88 in.