In a given circle a central angle of 40° intercepts a chord of 6 cm. What is the circumference of the circle?
∠B = ∠A = 70°.
| By the Law of Sines, the radius is | 6 | = | x | → | x | = | 6 sin 70° | . |
| sin 40° | sin 70° | sin 40° |
The circumference is 2 r, or |
2 · 6 sin 70° |
= | 12 · sin 70° |
≈ | 12 (3.14)(.94) |
| sin 40° | sin 40° | .64 |
≈ 55.34 cm