The Law of Cosines

The Law of Cosines

The Law of Cosines is the relationship between sides and angles in any triangle.

Introduction

  • Draw a triangle ABC, then draw three squares on three sides.
  • Draw three lines through A,B,and C so that each line is perpendicular to the opposite side.
  • The proof for A1=A2, A3=A4, and A5=A6 is provided by the applet bellow.

Applet

How to use the applet.
  • Drag the red points to change the shape of the triangle.
  • Select a rectangle from "green", "pink", and "blue".
  • Press ">" button to transform the rectangle.
Activity
  1. Transform A1 to A2.
  2. Transform A3 to A4.
  3. Transform A5 to A6.
  4. See the visual proof for "The Law of Cosines"
Mr. KOBAYASHI Akira at Seisan Circle(a math education research group) told us the idea of the applet.