Law of Sines Explained Visually | The Hidden Circle Behind a/sin A

Why does a divided by sin A equal the same value for every side of a triangle? Move a vertex around its circumcircle, add a diameter, and watch a right triangle reveal the answer. We connect each side to its opposite angle, derive the extended sine rule a/sin A = b/sin B = c/sin C = 2R, and explain the obtuse-angle case. Two worked exercises show how to find a chord and how to recover the circumradius. Original practice for students building trigonometry and precalculus skills. These exercises are not reproduced official exam questions. Chapters 00:00 One chord and a moving vertex 00:21 Match sides and opposite angles 00:51 Add a diameter 01:21 Read the sine ratio 01:53 Build the extended sine rule 02:24 What about obtuse angles 02:50 Practice 1 Find the chord 03:18 Practice 1 Solution 03:44 Practice 2 Find the radius 04:07 Practice 2 Solution 04:31 Remember the diameter Pause at each practice question and try it before following the solution. Which visual step helped the formula make sense? Tell us in the comments. Subscribe to Math Is Art for visual math lessons and step-by-step practice. Turn on notifications if you would like alerts for new lessons. See it. Understand it easily. #LawOfSines #Trigonometry #MathIsArt #visualmath