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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

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

Grade:12

2 Answers

Arun
25750 Points
3 years 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
3 years 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)

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