Question

question 3 of 25 in △pqr, m∠p = 60°, m∠q = 30°, and m∠r = 90°. which of the following statements about △pqr are true? check all that apply. a. pq = 2·pr b. qr = 2·pr c. qr = $\frac{sqrt{3}}{2}$·pq d. qr = $sqrt{3}$·pr e. pq = $sqrt{3}$·pr f. pr = $\frac{sqrt{3}}{2}$·pq

Explanation:

Step1: Identify triangle type

30-60-90 right triangle, hypotenuse PQ (opposite 90°), PR opposite 30°, QR opposite 60°.

Step2: Assign side lengths

Let PR = x (opposite 30°). Hypotenuse PQ = 2x, QR = x√3 (opposite 60°).

Step3: Check each option

A: PQ=2·PR → 2x=2x ✔️; B: QR=2·PR → x√3≠2x ❌; C: QR=(√3/2)·PQ → x√3=(√3/2)(2x) ✔️; D: QR=√3·PR → x√3=√3·x ✔️; E: PQ=√3·PR → 2x≠√3 x ❌; F: PR=(√3/2)·PQ → x≠√3 x ❌.

Answer:

A. PQ=2·PR, C. QR=√3/2·PQ, D. QR=√3·PR