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 $6$ $6$ 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 $\frac{π}{8}$ $pi/8$ . If side C has a length of $6$ $6$ 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 · 2017-11-25T15:48:41

$A = \frac{6 sin (\frac{π}{12})}{sin (\frac{π}{8})} ≅ 4.06$ $A=(6sin(pi/12))/sin(pi/8)~=4.06$

Explanation:

We can use the the Law of sines, which states that the ratio of the length of a side to the sine of its opposite angle is equal for all sides and angles in a triangle. You can also express this using the following equation:

$\frac{sin (α)}{a} = \frac{sin (β)}{b} = \frac{sin (γ)}{c}$ $sin(alpha)/a=sin(beta)/b=sin(gamma)/c$

where $α$ $alpha$ is the opposite side to $a$ $a$ , $β$ $beta$ is the opposite side to $b$ $b$ and $γ$ $gamma$ is the opposite side to $c$ $c$ .

If you draw up the triangle, you can see that $\frac{π}{8}$ $pi/8$ is the angle opposite $C$ $C$ and $\frac{π}{12}$ $pi/12$ is the angle opposite $A$ $A$ . Using the Law of sines, we can setup the following equation:

$\frac{sin (\frac{π}{8})}{6} = \frac{sin (\frac{π}{12})}{A}$ $sin(pi/8)/6=sin(pi/12)/A$

$A sin (\frac{π}{8}) = 6 sin (\frac{π}{12})$ $Asin(pi/8)=6sin(pi/12)$ (using cross-multiplication)

$A = \frac{6 sin (\frac{π}{12})}{sin (\frac{π}{8})} ≅ 4.06$ $A=(6sin(pi/12))/sin(pi/8)~=4.06$

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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 $6$ $6$ 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/8π8pi/8. If side C has a length of 6 66 and the angle between sides B and C is pi/12π12pi/12, what is the length of side A?

1 Answer

Explanation:

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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 $6$ $6$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?