Question

ordering 5 points
in △pqr, pq = 11 ft, qr = 7 ft, and pr = 15 ft. order the angles from least to greatest.
(hint draw it out & label first!)
1 ≡ ∠q
2 ≡ ∠r
3 ≡ ∠p

Explanation:

Step1: Recall the triangle angle - side relationship

In a triangle, the larger the side opposite an angle, the larger the angle. So we first need to identify which side is opposite each angle.

• For \(\angle P\), the side opposite to it is \(QR\). Given \(QR = 7\) ft.
• For \(\angle Q\), the side opposite to it is \(PR\). Given \(PR=15\) ft.
• For \(\angle R\), the side opposite to it is \(PQ\). Given \(PQ = 11\) ft.

Step2: Order the lengths of the opposite sides

First, order the lengths of the sides: \(QR=7\) ft, \(PQ = 11\) ft, \(PR=15\) ft. So \(QR

Step3: Order the angles based on opposite sides

Since the larger the side opposite an angle, the larger the angle, the angles opposite these sides will follow the same order.

• The side opposite \(\angle P\) is \(QR\) (length 7 ft), the side opposite \(\angle R\) is \(PQ\) (length 11 ft), and the side opposite \(\angle Q\) is \(PR\) (length 15 ft).
• So the order of the angles from least to greatest is \(\angle P<\angle R<\angle Q\).

Answer:

\(\angle P<\angle R<\angle Q\)