a triangle has area 30,one side of lenth 10,and the median to that side of length9.let theta be the acute angle formed by that side and the median.the value of sin theta ,is

Dear Abhinav,

We know area of a triangle is 1/2.a.b.sin x...where x is the angle between ab,So
area of the whole triangle=sum of areas of the two triangles formed by median.
                                         =1/2.5.9.sin x + 1/2.5.9.sin(180-x)
                                         =45.sin x
BUT AREA=30
hence 45sin x = 30
=> sin x = 30/45 = 2/3 (ANS)

Regards.