Problem preview
G-C.5 Warmup M2-033-A08-V01

Derive arc length and sector area formulas using similarity; define radians and convert degrees/radians.

Find a central angle in radians from arc length and radius

Problem

Find the central angle from arc length \(12\) and radius \(6\).

Big Picture

What this problem is really about

A radian angle is the ratio of intercepted arc length to radius, so the two length units should cancel. We’ll isolate the angle in the arc-length relationship, divide the sourced measures in the correct order, and reconstruct the arc to verify the result.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-C.5
Category
Geometry
Domain
Circles
Objective
Derive arc length and sector area formulas using similarity; define radians and convert degrees/radians.
Problem type
Find a central angle in radians from arc length and radius