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a triangle has area 30,one side of length 9.let theta be the acute angle formed by that side and the median. the value of sin theta,is

Arun
25763 Points
one year ago
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)
Vikas TU
14149 Points
one year ago

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)