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Grade 12IIT JEE Entrance Exam

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

Profile image of Abhinav Saurabh
13 Years agoGrade 12
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2 Answers

Profile image of Arun
6 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)
Profile image of Vikas TU
5 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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