In triangle PQR m angle P=60°, and m angle Q=30°, and m angle R=90°. Which of the following statements about triangle PQR are true? Check all that apply.

The correct statements about triangle PQR.are given by options A), B), and F) and this can be determined by using the trigonometric functions.

Given :

In triangle PQR, angle P is 60°, angle Q is 30° and angle R is 90°.

The trigonometric functions can be used in order to determine the correct statements about triangle PQR.

[tex]\rm sin30 = \dfrac{PR}{QP}[/tex]

[tex]\rm PQ = 2\;PR[/tex]

[tex]\rm cos30 = \dfrac{QR}{QP}[/tex]

[tex]\rm PR=\dfrac{\sqrt{3} }{2}\;PQ[/tex]

[tex]\rm tan30 = \dfrac{PR}{QR}[/tex]

[tex]\rm \sqrt{3}\; PR= QR[/tex]

[tex]\rm sin60 = \dfrac{QR}{PR}[/tex]

[tex]\rm QR=\dfrac{\sqrt{3} }{2} \;PR[/tex]

[tex]\rm cos60 = \dfrac{PR}{QP}[/tex]

[tex]\rm PR=2\;PQ[/tex]

[tex]\rm tan60 = \dfrac{QR}{PR}[/tex]

[tex]\rm PR=\sqrt{3} \; QR[/tex]

Therefore, the correct option A), B), and F).

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