One acute angle of a right angled triangle is double the

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One acute angle of a right angled triangle is double the other. If the length of its hypotenuse is 10 cm, then its area is

From ∆ABC

sin 30° =	AB
	AC

⇒	1	=	AB
	2		AC

⇒ AB =	1	AC =	1	× 10 = 5 cm.
	2		2

∴ BC = √AC² - AB² = √10² - 5²
= √100 - 25 = √75
= 5√3 cm
∴ Area of ∆ABC

=	1	× AB × BC
	2

=	1	× 5 × 5√3 =	25√3	cm²
	2		2

	25	√3 cm²
	2