If sides A and B of a triangle have lengths of 13 and 2 respectively, and the angle between them is #(pi)/6#, then what is the area of the triangle?

1 Answer
Feb 6, 2016

First we solve #pi/6#
#pi=180^circ#

So,

#rarr=180/6=45^circ#

Now we consider the diagram:

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The formula for finding the area of triangle when given two sides of a triangle and the angle between them=#1/2 ab sinC=(ab sinC)/2#

In this case #a=13,b=2,C=45^circ#

#sin C=sin(45^circ)=sqrt2/2#

#rarrArea=((13)(2)(sqrt2/2))/2#

#rarrArea=(26(sqrt2/2))/2#

#rarrArea=((52sqrt2)/2)/2#

#rarrArea=(26sqrt2)/2=13sqrt2 #