Chapter 8.2, Problem 7AYU

To determine

To find: Whether the given statement is true or false.

Explanation of Solution

Given information:

The given statement is, “The Law of Sines can be used to solve triangles where three sides are known”.

Concept used:

For a triangle with sides a , b , c and opposite angles A , B , C , the Law of Sines state that

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

Law of Cosines:

If ABC is a triangle with sides $a$ , $b$ , and $c$ , then

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

If only three sides of the triangle are known than it is not possible to solve the triangle, at least one angle is required. It can be solved by using cosine rule.

Thus, the given statement is false.