Chapter 14.5, Problem 5LC

Solution

To describe:The Law of Sine and Cosines for finding measure of the missing angle or side of a triangle.

Given data: One missing side or angle of a triangle is to be found using Law of Sine or Cosine.

Method/Formula used:

The Law of Sine states that in a triangle ABC, shown in Fig.1.

  

  $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

The Law of Cosine states,

  $\cos A=\frac{b^2+c^2-a^2}{2bc}$

Description:

Suppose two sides a , b and one angle B of a triangle is given then using Sine law angle A can be found as:

  $\sin A=\frac{a\sin B}{b}=\frac{\sin C}{c}$

If two angles A , B and one side b of a triangle is given then using Sine law side a can be found as:

  $b=\frac{a\sin B}{\sin A}$

If two sides a , b and one angle C of a triangle is given then using Cosine law side c can be found as:

  $\begin{array}{c}\cos C=\frac{a^2+b^2-c^2}{2ab}\\ c^2=a^2+b^2-2ab\cos C\\ c=\sqrt{a^2+b^2-2ab\cos C}\end{array}$

If three sides a , b , and c are given then angle A can be found as:

  $\cos A=\frac{b^2+c^2-a^2}{2bc}$