Answer: RS = 6, PS = \(6\sqrt3\)
In Δ PSR, ∠S = 90º, ∠P = 30º, so ∠R = 60º; it is a 30º–60º–90º triangle.
Side opposite 30º = \(\tfrac12\) × hypotenuse: RS = \(\tfrac12 \times 12\) = 6.
Side opposite 60º = \(\tfrac{\sqrt3}{2}\) × hypotenuse: PS = \(\tfrac{\sqrt3}{2} \times 12 = 6\sqrt3\) (≈ 10.38).