A triangle has sides A, B, and C. The angle between sides A and B is $\frac{2 π}{3}$ $(2pi)/3$ . If side C has a length of $12$ $12$ 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 · 2016-02-16T08:15:17

$a = 3.5863$ $a=3.5863$ units

Given Two Angles and a side opposite one of them. Use Sine Law

Given: Angle $C = \frac{2 π}{3}$ $C=(2pi)/3$ and angle $A = \frac{π}{12}$ $A=pi/12$
side $c = 12$ $c=12$

Solve for side $a$ $a$ :

From Sine Law: $\frac{a}{sin A} = \frac{c}{sin C}$ $a/sin A=c/sin C$

$a = \frac{c \cdot sin A}{sin C} = \frac{12 \cdot sin (\frac{π}{12})}{sin (\frac{2 π}{3})}$ $a=(c*sin A)/sin C=(12*sin(pi/12))/sin ((2pi)/3)$

$a = 3.5863$ $a=3.5863$

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A triangle has sides A, B, and C. The angle between sides A and B is (2pi)/32π3(2pi)/3. If side C has a length of 12 1212 and the angle between sides B and C is pi/12π12pi/12, what is the length of side A?