Memorization Techniques for Peter Chew Rule

Abstract

We normally use sine rule to find the opposite side angle given when we are given two angles and one side. We also can use sine rules to find non-included angle when we are given two sides and a non-included angle. However, sine rule is not suitable to find the included angle when we are given three sides or to find the third side when we are given two sides and the included angle. This is because if we use the sine rule, the equation will have 2 unknowns. As we know, an equation with 2 unknowns cannot be solved. Therefore, we need to learn Cosine rule to solve the above problem. When giving 2 sides and an included angle, the sine rule and the cosine rule also are not suitable for finding the non-included angle directly. This is because if you use a sine rule or a cosine rule, the equation will have 2 unknowns. As mentioned earlier, equations with 2 unknowns cannot be solved. Therefore, we need to learn Peter Chew rule to solve the above problem. Peter Chew Rule allows us to find non included angles directly, more easier and more accurate. Symmetry, we can get 3 similar sine rules, 3 similar cosine rules and 6 similar Peter Chew rules. A Memorization Techniques must be created to make us happily remember 6 similar Peter Chew rules. For sine rule, a/sin⁡A = b/sin⁡B = c/sin⁡C . Techniques to remember rules is sides versus angles. If the angle we are looking for is A, then the side is also a. As same, If the angle we are looking for is B, then the side is also b. For cosine rule, a^2 = b^2 〖+ c〗^2 -2 bc cos⁡A. If the side we are looking for is a ,then the angle given normally is also A .As with the sine and cosine rules, the memorization techniques to remember Peter Chew rules, A = (a sin B)/(c - a cos B) , is also sides versus angles. If the angle we are looking for is A, then for the right hand side, the side is also a. If the angle is known as B, then for the denominator, the other side is c. the denominator will be c - a cos B. If the angle is known as C, the other side of the denominator is b, the denominator will be b - a cos C. Therefore, Peter Chew rule is tan A = (a sin C)/(b - a cos C) . So the technique to remember is very simple, the denominator will involve a, b, c. Therefore, remembering Peter Chew's rules is as easy as remembering a, b, and c. A game will be developed to test the efficiency of Peter Chew Rule's memorization techniques.