A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{4}$ $pi/4$ . If side C has a length of $1$ $1$ 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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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{4}$ $pi/4$ . If side C has a length of $1$ $1$ 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 · 2017-07-22T14:26:29

The length of the side $a = 0.37$ $a=0.37$

Explanation:

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The angles are

$ˆ C = \frac{1}{4} π$ $hatC=1/4pi$

$ˆ A = \frac{1}{12} π$ $hatA=1/12pi$

$ˆ B = π - (\frac{1}{4} π + \frac{1}{12} π) = π - (\frac{3}{12} π + \frac{1}{12} π) = \frac{8}{12} π = \frac{2}{3} π$ $hatB=pi-(1/4pi+1/12pi)=pi-(3/12pi+1/12pi)=8/12pi=2/3pi$

The side $c = 1$ $c=1$

We apply the sine rule to the triangle

$\frac{a}{sin ˆ A} = \frac{b}{sin ˆ B} = \frac{c}{sin ˆ C}$ $a/sin hatA=b/sin hatB=c/sin hatC$

$\frac{a}{sin (\frac{1}{12} π)} = \frac{b}{sin (\frac{2}{3} π)} = \frac{1}{sin (\frac{1}{4} π)}$ $a/sin (1/12pi)=b/sin (2/3pi)=1/sin (1/4pi)$

Therefore,

$a = \frac{sin (\frac{1}{12} π)}{sin (\frac{1}{4} π)} = 0.37$ $a=sin(1/12pi)/sin(1/4pi)=0.37$

$b = \frac{sin (\frac{2}{3} π)}{sin (\frac{1}{4} π)} = 1.22$ $b=sin(2/3pi)/sin(1/4pi)=1.22$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{4}$ $pi/4$ . If side C has a length of $1$ $1$ 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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A triangle has sides A, B, and C. The angle between sides A and B is pi/4π4pi/4. If side C has a length of 1 11 and the angle between sides B and C is pi/12π12pi/12, what is the length of side A?

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