A triangle has sides A, B, and C. The angle between sides A and B is $pi/4$ . If side C has a length of $1$ and the angle between sides B and C is $pi/12$ , what is the length of side A?

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Answer 1 · 2017-07-22T14:26:29

The length of the side $a=0.37$

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The angles are

$hatC=1/4pi$

$hatA=1/12pi$

$hatB=pi-(1/4pi+1/12pi)=pi-(3/12pi+1/12pi)=8/12pi=2/3pi$

The side $c=1$

We apply the sine rule to the triangle

$a/sin hatA=b/sin hatB=c/sin hatC$

$a/sin (1/12pi)=b/sin (2/3pi)=1/sin (1/4pi)$

Therefore,

$a=sin(1/12pi)/sin(1/4pi)=0.37$

$b=sin(2/3pi)/sin(1/4pi)=1.22$

A triangle has sides A, B, and C. The angle between sides A and B is pi/4pi/4. If side C has a length of 1 1 and the angle between sides B and C is pi/12pi/12, what is the length of side A?