Law of Cosines Explorer
GOAL: See how the Law of Cosines uses two sides and their included angle to determine the opposite side.
INSTRUCTIONS: Drag the vertices to change the triangle, choose a side to calculate, and follow the updated steps to verify the result.
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 Cosines
The Law of Cosines states:
a² = b² + c² − 2bc cos(A)
b² = a² + c² − 2ac cos(B)
c² = a² + b² − 2ab cos(C)
✨ Notice
The Law of Cosines relates the sides and angles of any triangle. When the angle is 90°, it reduces to the Pythagorean theorem (cos(90°) = 0)!
💡 How to Use
- • Drag any vertex (A, B, C) to reshape the triangle
- • Watch how the calculations update in real-time
- • Switch between calculating different sides
- • Verify that the formula correctly predicts each side length!