Question

in triangle pqr, ∠p = 105°, ∠q = 35°, and ∠r = 40°. order the sides of the triangle from shortest to longest.
a) pq, pr, qr
b) qr, pr, pq
c) pr, pq, qr
d) qr, pq, pr

1. the sides of a triangle are 3 meters, 5 meters, and 7 meters. which angle is opposite the longest side?

a) the angle opposite the 3 - meter side.
b) the angle opposite the 5 - meter side.
c) the angle opposite the 7 - meter side.
d) it is impossible to determine.

Explanation:

Step1: Recall angle - side relationship

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

Step2: Identify smallest to largest angles in triangle PQR

Given $\angle Q = 35^{\circ}$, $\angle R=40^{\circ}$, $\angle P = 105^{\circ}$. So, $\angle Q<\angle R<\angle P$.

Step3: Determine corresponding sides

The side opposite $\angle Q$ is $PR$, the side opposite $\angle R$ is $PQ$, and the side opposite $\angle P$ is $QR$. So, the order of sides from shortest to longest is $PR, PQ, QR$.

Step4: For the second - question

In a triangle, the angle opposite the longest side is the largest angle. Given side lengths 3 meters, 5 meters, and 7 meters, the longest side is 7 meters. So the angle opposite the 7 - meter side is the angle we are looking for.

Answer:

1. c) PR, PQ, QR
2. c) The angle opposite the 7 - meter side.