Law of Sines Explorer

GOAL: Discover that each side length divided by the sine of its opposite angle stays equal in every triangle.

INSTRUCTIONS: Drag the vertices to reshape the triangle, then compare the three ratio calculations; use the Labels and Angles buttons to focus your view.

Interactive Triangle

         Side a (opposite A)
        
         0.0

         Side b (opposite B)
        
         0.0

         Side c (opposite C)
        
         0.0

         Angle A
        
         0.0°

         Angle B
        
         0.0°

         Angle C
        
         0.0°

Law of Sines

The Law of Sines states:

a / sin(A) = b / sin(B) = c / sin(C)

Ratio Calculations

a / sin(A)

0.0 / 0.000 = 0.00

b / sin(B)

0.0 / 0.000 = 0.00

c / sin(C)

0.0 / 0.000 = 0.00

✨ Notice

All three ratios are equal! This relationship holds true for ANY triangle. Try dragging the vertices to create different triangles and watch the ratios stay equal.

💡 How to Use

• Drag any vertex (A, B, C) to reshape the triangle
• Watch how side lengths and angles change
• Observe that all three ratios remain equal
• Each color connects angles to their opposite sides