Chapter 6, Problem 132CR

To determine

True or false:

The solution by using the law of sines is always unique.

Answer to Problem 132CR

False. The solution by using the law of sines is not always unique.

Explanation of Solution

Given information:

The given statement is:

‘The solution by using the law of sines is always unique.’

The law of sines is given by the following expression:

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

The law of sines is applicable to various cases of triangles in which one of angle is defined as obtuse, acute or right angle.

By using the sines law, the solution is not always unique because there are possible cases in which the values of $a,b,c$ varies.

Consider;

  $a$ is greater than the height $h$ of the triangle but less than other side $b$ , in this case there is result of two solutions by using sines law.

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

The solution by using the law of sines is not always unique solution.