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In a ABC triangle the medians AD and BE are drawn such that AD =4 angle BAD is 30° and angle ABE is 60° then find the area of the triangle

In a ABC triangle the medians AD and BE are drawn such that AD =4 angle BAD is 30° and angle ABE is 60° then find the area of the triangle

Grade:11

1 Answers

nitish
36 Points
4 years ago
consider the point of intersection of AD and BE as O.
now as BAD=30 and ABE is 60
therefore AOB=90.
also we know that median divides a triangle into two equal areas.
area of ABD=area of ADC
 
also O is centroid.
therefore AO=(2*4/3)=8/3
 
sin(60)=AO/AB
AB=16/(3*root(3))
 
now you know AD,AB  and angle between the two i.e. 30
 
so area(ABD) =1/2*AB*AD*sin(theta)= 16/(3*root(3))
(theta=30)
therefore, the total area =2(area(ABD))
=32/(3*root(3))
 

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