Question

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find the shortest side of $\triangle pqr$, given that $m\angle r = 86^\circ$, $m\angle p = 51^\circ$, and $m\angle q = 43^\circ$.

Explanation:

Step1: Recall triangle side-angle relation

In a triangle, the shortest side is opposite the smallest angle.

Step2: Identify the smallest angle

Given angles: \( m\angle R = 86^\circ \), \( m\angle P = 51^\circ \), \( m\angle Q = 43^\circ \). The smallest angle is \( \angle Q = 43^\circ \).

Step3: Determine the side opposite the smallest angle

In \( \triangle PQR \), the side opposite \( \angle Q \) is \( PR \).

Answer:

\( PR \)