1.

Two medians drawn from acute angles of a right angled triangles intersect at an angle pi//6. If the length of the hypotenuse of the triangle is 3 units, then area of the traingle (in sq. units) is

Answer»

`SQRT(3)`
3
`sqrt(2)`
9

Solution :`because ""AC=3impliesa^(2)+b^(2)=9`
SLOPE of `AD=(-2b)/(a)`
Slope of `CF=(-b)/(2a)`
`therefore""tan.(pi)/(6)=|(-(2b)/(a)+(b)/(2a))/(1+(b^(2))/(a^(2)))|=|(-3ab)/(2(a^(2)+b^(2)))|=(3ab)/(9xx2)=(1)/sqrt(3)=(ab)/(6)impliesab=2sqrt(3)`
`DeltaABC = (1)/(2)ab=sqrt(3)`


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