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Algebra Difficulty 2.0 Junior Prove it Canada

Suppose $0^\circ < x < 90^\circ$ and $2\sin^2 x + \cos^2 x = \frac{25}{16}$ . What is the value of $\sin x$ ?

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.