\( P Q R S \) is a quadrilateral rightangled at \( P \) and at \( S . T \) is a point on the diagonal \( P R \) and \( S T \) is perpendicular to \( P R \). The angles \( T P Q, T S P, T R S \) and \( T Q R \) are \( 30^{\circ} . P S=1 \) unit. The length of \( P Q \) could be (A) \( \sqrt{2}+\sqrt{3} \) (B) \( 2 \sqrt{3}-1 \) (C) \( \sqrt{3}+1 \) (D) \( \sqrt{3}-\sqrt{\sqrt{3}-1} \) (E) \( \sqrt{3}+\sqrt{\sqrt{3}-1} \)
Added by Carmen S.
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The angles \(TPQ\), \(TSP\), \(TRS\), and \(TQR\) are all \(30^\circ\). Also, \(PS = 1\) unit. Show moreβ¦
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