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Question
In ΔPQR, ∠P = 30°, ∠Q = 60°, ∠R = 90° and PQ = 12 cm, then find PR and QR.
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Solution
From figure using the definition of sin
sin∠P = `"RQ"/"PQ"`
∴ sin30° = `"RQ"/12`
∴ `1/2 = "RQ"/12`
∴ RQ = 12/2 = 6 cm
∴ QR = 6 cm
sin∠Q = `"PR"/"PQ"`
∴ sin 60° = `"PR"/12`
∴ `sqrt(3)/2 = "PR"/12`
∴ PR = `(12sqrt(3))/2`
∴ PR = `6sqrt3` cm
Therefore PR = `6sqrt3` cm and QR = 6 cm
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