Question

item 21
given \\( \triangle r s t \\) with \\( r s=18 \mathrm{~cm}, s t=12 \mathrm{~cm} \\), and \\( r t=27 \mathrm{~cm} \\), which of the following statements is true about the angles of this triangle?
a. the measure of \\( \angle r \\) is the least.
b. the measure of \\( \angle s \\) is the least.
c. the measure of \\( \angle r \\) is the greatest.
d. the measure of \\( \angle t \\) is the greatest.

Explanation:

Step1: Recall the triangle side - angle relationship

In a triangle, the larger side is opposite the larger angle.

Step2: Compare the side lengths

We have \(RS = 18\mathrm{cm}\), \(ST=12\mathrm{cm}\), and \(RT = 27\mathrm{cm}\).
Since \(ST

Step3: Determine the angles opposite the sides

\(\angle R\) is opposite \(ST\), \(\angle T\) is opposite \(RS\), and \(\angle S\) is opposite \(RT\).
Because \(ST\) is the shortest side, the angle opposite to it (\(\angle R\)) is the least.

Answer:

A. The measure of \(\angle R\) is the least.