The measure of PQ is 12.72
Explanation:
We have the right triangle ΔPQR and we want to know the measure of PQ. PQ is opposite to ∠R, so from trigonometry we know that:
[tex]sin(\alpha)=\frac{Opposite \ side}{Hypotenuse} \\ \\ \\ Here: \\ \\ \alpha=m\angle R=58^{\circ} \\ \\ Opposite \ side=\overline{PQ} \\ \\ Hypotenuse=\overline{RQ}=15 \\ \\ \\ So: \\ \\ sin(58^{\circ})=\frac{\overline{PQ}}{15} \\ \\ \\ Isolating \ \overline{PQ}: \\ \\ \overline{PQ}=15sin(58^{\circ}) \\ \\ \overline{PQ}=15(0.848)\\ \\ \boxed{\overline{PQ}=12.72}[/tex]
Learn more:
Right triangles: https://brainly.com/question/10252821
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