The triangles are right triangles, then we can apply Pytagoras´ theorem.
Solution is:
The triangles are similar
From the attached picture, and from parameterization concepts
RS = μ × RQ 0 < μ < 1
From Δ PRQ sinα = RQ/PR PQ = h₁ ( hypothenuse in Δ PRQ)
From Δ RST sinα = RS/ST ST = h₂ ( hypothenuse in Δ RST)
Then RQ/h₁ = RS/h₂
or RQ × h₂ = RS × h₁ ⇒ h₂ = (RS/RQ) × h₁ ⇒ h₂ = μ × h₁
Then both hypothenuse are proportional, it follows both triangles are similar
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