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?

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Answer 1 · 2016-02-06T06:04:45

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

So,

$rarr=180/6=45^circ$

Now we consider the diagram:

enter image source here

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 $a=13,b=2,C=45^circ$

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

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

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

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

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

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