Trigonometry

Question

What is the cosine rule? What would you use it for practically?

Answer

The law of cosines gives a relationship between the three sides of a triangle and one of the angles. If the sides have lengths of A, B, and C, and the angle opposite the C side is called theta, then c*c = a*a + b*b - 2 ab cos(theta) The Pythagorean theorem is a special case of the law of cosines. When theta is 90 degrees, the 2 ab cos(theta) term goes to zero. A practical application is any time that you have a triangle and know three out of these four quantities, you can find the fourth one. Suppose you were building a fence around your yard, and you want to build a 90 degree corner. You could take a 3-foot section of fence, a 4-foot section of fence, and a 5-foot piece of rope. Tie the rope to each of the free ends of the fence and connect the fence pieces together. Pull the rope tight, and you will have a 90 degree angle in your fence. There are some applications to this in radio communications. Radio signals are transmitted over sine waves, and there are many trigonometry applications in radio because the signals are represented as sine functions.