Question

question 7
find the measure of the hypotenuse and the opposite side in the right triangle pqr.
image of right triangle pqr with right angle at q, qr = 12 cm, angle at r is 45°

Explanation:

Step1: Identify triangle type

It's a 45 - 45 - 90 right triangle (since one angle is \(45^\circ\), right angle at Q, so the other angle at P is also \(45^\circ\)). In a 45 - 45 - 90 triangle, the legs are equal, and hypotenuse \(= \text{leg} \times \sqrt{2}\).
Given leg \(QR = 12\) cm, so leg \(PQ\) (opposite to \(\angle R\)) is also 12 cm.

Step2: Calculate hypotenuse \(PR\)

Using the formula for hypotenuse in 45 - 45 - 90 triangle: \(PR=QR\times\sqrt{2}\)
Substitute \(QR = 12\) cm: \(PR = 12\sqrt{2}\) cm (or approximately \(12\times1.414 = 16.968\) cm).

Answer:

Opposite side ( \(PQ\) ) to \(\angle R\) is \(12\) cm. Hypotenuse ( \(PR\) ) is \(12\sqrt{2}\) cm (or approximately \(16.97\) cm).