A triangle has sides A, B, and C. The angle between sides A and B is $\frac{7 π}{12}$ $(7pi)/12$ . If side C has a length of $2$ $2$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?

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Answer 1 · 2017-02-25T07:23:50

$A = 2 \sqrt{3} - 4$ $A=2sqrt3-4$

You would apply the sine theorem to find the length of side A:

$\frac{A}{sin ˆ B C} = \frac{C}{sin ˆ A B}$ $A/sin hat(BC)=C/sin hat (AB)$

Then

$A = C \cdot \frac{sin ˆ B C}{sin ˆ A B}$ $A=C*sin hat(BC)/sin hat(AB)$

$A = \frac{2 \cdot sin (\frac{π}{12})}{sin (\frac{7 π}{12})}$ $A=(2*sin(pi/12))/sin((7pi)/12)$

$=(2*((sqrt2-sqrt6))/cancel4)/((sqrt2+sqrt6)/cancel4)$

$=(2(sqrt2-sqrt6)^2)/((sqrt2+sqrt6)(sqrt2-sqrt6))$

$=(2(sqrt2-sqrt6)^2)/(2-6)$

$=(cancel2(2+6-2sqrt12))/-cancel4^2$

$=-(cancel8^4-cancel2sqrt12)/cancel2$

$=sqrt12-4$

$=2sqrt3-4$

A triangle has sides A, B, and C. The angle between sides A and B is (7pi)/127π12(7pi)/12. If side C has a length of 2 22 and the angle between sides B and C is pi/12π12pi/12, what is the length of side A?