Chapter 12, Problem 4CUR

To determine

Tocheck:Whether the inequality $RT>RS$ is true or not.

Answer to Problem 4CUR

Yes, the inequality $RT>RS$ is true.

Explanation of Solution

Given information:

In $\Delta RST$ , if $m\angle R=48$ and $m\angle S=68$ .

In an triangle, the sum of all interior angles is $180°$ .

As given, $m\angle R=48$ and $m\angle S=68$ .

Simplify for the measure of third angle of triangle.

  $\begin{array}{c}\angle R+\angle S+\angle T=180\\ 48+68+\angle T=180\\ \angle T=180-68-48\\ \angle T=64\end{array}$

As the measure of angle $S$ is greater than the measure of angle $T$ . So, the measure of length of side $RT$ is greater than the measure of length of side $RS$ .

Therefore, the inequality $RT>RS$ is true.