A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{8}$ $pi/8$ . If side C has a length of $7$ $7$ 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 · 2017-07-04T06:05:47

The answer is $A = 4.7$ $A=4.7$

We apply the sine rule to the triangle $A B C$ $ABC$

$\frac{A}{sin ˆ A} = \frac{C}{sin ˆ C}$ $A/sin hatA=C/sin hatC$

The side $C = 7$ $C=7$

The angle $ˆ C = \frac{1}{8} π$ $hat C=1/8pi$

The angle $ˆ A = \frac{1}{12} π$ $hat A=1/12pi$

Therefore,

$A = C \cdot \frac{sin ˆ A}{sin ˆ C} = 7 \cdot \frac{sin (\frac{1}{12} π)}{sin (\frac{1}{8} π)}$ $A=C*sin hatA/sin hat C=7* sin(1/12pi)/sin(1/8pi)$

$= 4.7$ $=4.7$

A triangle has sides A, B, and C. The angle between sides A and B is pi/8π8pi/8. If side C has a length of 7 77 and the angle between sides B and C is pi/12π12pi/12, what is the length of side A?