Question

1. given the picture below, which is the longest side? (triangle with vertices p, r, q; angles at p: 15°, at r: 124°, at q: 41°)

Explanation:

Step1: Recall triangle angle-side relation

In a triangle, the longest side is opposite the largest angle. This is the Law of Sines (or basic angle-side proportionality: larger angle → longer opposite side).

Step2: Find the largest angle in △PQR

Given angles: \( \angle P = 15^\circ \), \( \angle R = 124^\circ \), \( \angle Q = 41^\circ \).
Compare the angles: \( 124^\circ > 41^\circ > 15^\circ \). So \( \angle R \) is the largest angle.

Step3: Identify the side opposite \( \angle R \)

In △PQR, side opposite \( \angle R \) is \( PQ \) (since \( \angle R \) is at vertex R, opposite side connects P and Q).

Answer:

The longest side is \( PQ \) (or the side opposite the \( 124^\circ \) angle, connecting vertices P and Q).