Chapter 6, Problem 134CR

To determine

True or false:

In addition to SSS and SAS, the law of cosines can be used to solve triangles with AAS conditions.

Answer to Problem 134CR

False. In addition to SSS and SAS, the law of cosines cannot be used to solve triangles with AAS conditions.

Explanation of Solution

Given information:

The given statement is:

‘In addition to SSS and SAS, the law of cosines can be used to solve triangles with AAS conditions.’

Consider,

A triangle $△ABC$ has three angles $\angle A,\angle B,\angle C$ and three sides $a,b,c$ .

Know that:

The law of cosines is given by the following expression:

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

As per the problem’s condition:

Known value: Two side: $a,b$ and one angle $\angle A$ .

That is if two sides and angle which is not included in the sides, then triangle is not able to solve by two sides and included angle.

Hence, the given statement is false. The correct statement is: