A vertical pole AB is standing at the centre B of a square

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A vertical pole AB is standing at the centre B of a square PQRS.If PR subtends an angle of 90° at the top, A of the pole, then the angle subtended by a side of the square at A is :

1. 30°
2. 45°
3. 60°
4. None of these

Correct Option: C

PA = PR
∠APB = ∠ARB = 45°
If PR = √2x :

PB =	x
	√2

From triangle APB ,

tan45° =	AB	⇒ AB = PB =	x
	PB		√2

∴ PA = √( x² / 2 ) + ( x² / 2 ) = √x² = x
∴ QA = PQ = PA = x
∴ ∠PAQ = 60°