Question

multiple choice 5 points
in the triangle below, which is the longest side?
triangle with vertices r, s, t; angle at r is 30°, angle at s is 80°; options: rs, rt, st

Explanation:

Step1: Find the third angle

In a triangle, the sum of interior angles is \(180^\circ\). Given \(\angle R = 30^\circ\) and \(\angle S = 80^\circ\), let \(\angle T=x\). Then \(30^\circ + 80^\circ+x=180^\circ\), so \(x = 180^\circ-(30^\circ + 80^\circ)=70^\circ\).

Step2: Relate angles to sides

In a triangle, the longest side is opposite the largest angle. The angles are \(30^\circ\) (opposite \(ST\)), \(80^\circ\) (opposite \(RT\)), and \(70^\circ\) (opposite \(RS\)). Since \(80^\circ\) is the largest angle, the side opposite to it (\(RT\)) is the longest.

Answer:

RT (the side opposite the \(80^\circ\) angle, as the largest angle in a triangle has the longest opposite side)