Chapter 9.6, Problem 3E

Solution

To decide: that to solve the triangle with the given case whether the law of sines or the law of cosines should be used.

Law of cosines

Given information:

The given case is:

SSS

Definition Used:

Law of Cosines:

If $△ABC$

has sides of length a , b , and c as shown, then:

  

  $\begin{array}{l}{a}^2=b^2+c^2-2bc\cos A\\ b^2=a^2+c^2-2ac\cos B\\ c^2=a^2+b^2-2ab\cos C\end{array}$

Law of Sines:

The law of sines can be written in either of the following forms for $△ABC$ with sides of length a , b and c .

  

  $\begin{array}{l}\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\\ \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\end{array}$

Explanation:

From the above definitions, it is clear that to use the law of sines at least one angle measure is required.

Since in the given case SSS, only the measure of side lengths of a triangle are known, so the only option here is to use the law of cosines 

Therefore, in this case, only the law of cosines can be used.