Chapter 8.6, Problem 58HP

To determine

To explain: The Las of Sines cannot used to solve a triangle for which we know three side lengths.

Answer to Problem 58HP

If we don’t know at least one angle, then it will be impossible to solve because there will be two unknown variable.

Explanation of Solution

Given information: The three sides of a triangle is given.

The Law of Sines is used to solve a triangle for which at least one angle is known. If we know only its three sides' length, then it is impossible to solve.

Example:

  $\frac{\sin A}{5}=\frac{\sin B}{2}$

Here, two variables are unknown, so it is impossible to solve them.