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 $16$ $16$ 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 $\frac{7 π}{12}$ $(7pi)/12$ . If side C has a length of $16$ $16$ 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 · 2016-01-05T05:53:00

$a = 4.28699$ $a=4.28699$ units

Explanation:

First of all let me denote the sides with small letters a, b and c
Let me name the angle between side "a" and "b" by $∠ C$ $/_ C$ , angle between side "b" and "c" $∠ A$ $/_ A$ and angle between side "c" and "a" by $∠ B$ $/_ B$ .

Note:- the sign $∠$ $/_$ is read as "angle".
We are given with $∠ C$ $/_C$ and $∠ A$ $/_A$ .

It is given that side $c = 16 .$ $c=16.$

Using Law of Sines
$\frac{sin ∠ A}{a} = \frac{sin ∠ C}{c}$ $(Sin/_A)/a=(sin/_C)/c$

$\Rightarrow \frac{sin (\frac{π}{12})}{a} = \frac{sin (\frac{7 π}{12})}{16}$ $implies Sin(pi/12)/a=sin((7pi)/12)/16$

$\Rightarrow \frac{0.2588}{a} = \frac{0.9659}{16}$ $implies 0.2588/a=0.9659/16$

$\Rightarrow \frac{0.2588}{a} = 0.06036875$ $implies 0.2588/a=0.06036875$

$\Rightarrow a = \frac{0.2588}{0.06036875} = 4.28699 \Rightarrow a = 4.28699$ $implies a=0.2588/0.06036875=4.28699 implies a=4.28699$ units

Therefore, side $a = 4.28699$ $a=4.28699$ units

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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 $16$ $16$ 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 $\frac{7 π}{12}$ $(7pi)/12$ . If side C has a length of $16$ $16$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?