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In a polar coordinate system, the vertices of a triangle are at (6,30 degrees), (2, 90 degrees), and (4, 150 degrees).  Find the area of this triangle.

 Dec 18, 2019
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We can convert the polar coordinates to  rectangular coordinates

 

(6,30)  =  (6cos 30, 6 sin30) =  ( 3 √3 , 3)  = A

(2, 90)  =  (0, 2)   = B  

(4,150)  =  ( 4cos 150 , 4 sin 150)  = (- 2 √3, 2)  = C

 

 

 

We  can let BC  be the base  = 2 √3

And the height  = 1

 

So....the area  =

 

(1/2) * (2 √3) (1)  =    √3 units^2

 

cool  cool  cool

 Dec 18, 2019

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