Chapter 6.2, Problem 62E

To determine

Whether the given statement is true or false.

Answer to Problem 62E

The statement is false.

Explanation of Solution

Given:

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

According to the law of the cosines, for the triangle with the sides a,b and c and angles A,B,C opposite to the sides a,b and c, then:

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

Hence, if the SSA is known that if two sides of the triangle and the one angle which is not included in the sides, hence, the law of the cosines cannot be use to solve the triangle as the formula having two sides and including angle.

Therefore, the statement is false.