In a right angled triangle ∆PQR, PR is the hypotenuse

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In a right angled triangle ∆PQR, PR is the hypotenuse of length 20 cm, ∠PRQ = 30°, the area of the triangle is

sin 30° =	PQ
	PR

⇒	1	=	PQ
	2		20

⇒ PQ = 20 ×	1	= 10 cm.
	2

cos 30° =	QR
	PR

⇒	√3	=	QR
	2		20

⇒ QR =	√3	× 20 = 10√3 cm.
	2

∴ Area of triangle PQR

=	1	× 10 × 10√3
	2

= 50√3 square cm.