Question

1. find the unknown side of the triangle below.

Explanation:

Step1: Identify triangle type and sides

Right triangle \(PQR\): hypotenuse \(PQ=31m\), leg \(QR=14m\), unknown leg \(PR=x\).

Step2: Apply Pythagorean theorem

\(PR^2 + QR^2 = PQ^2\) → \(x^2 + 14^2 = 31^2\)

Step3: Calculate squares

\(x^2 + 196 = 961\)

Step4: Solve for \(x^2\)

\(x^2 = 961 - 196 = 765\)

Step5: Compute \(x\)

\(x = \sqrt{765} \approx 27.66\)

Answer:

Approximately 27.7 m (or exactly \(3\sqrt{85}\) m)