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 $2$ $2$ 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 $2$ $2$ 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 · 2016-01-05T06:02:10

The length of $a$ $a$ is $\frac{4}{3}$ $4/3$

Explanation:

We are able to solve it using logic:
Since $\frac{π}{8} = 2$ $pi/8 = 2$ we'll multiply both sides by 8 resulting in $π = 16$ $pi = 16$ .

Then, another logic: $π = 16$ $pi = 16$ , so $\frac{π}{12} = \frac{16}{12} = \frac{4}{3}$ $pi/12 = 16/12 = 4/3$ .

I won't say units, its implicit.

Answer 2 · 2016-01-05T06:03:29

$a = 1.3524$ $a=1.3524$ 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 $c = 2 .$ $c=2.$

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

$\Rightarrow \frac{sin (\frac{π}{12})}{a} = \frac{sin (\frac{π}{8})}{2}$ $implies Sin(pi/12)/a=sin((pi)/8)/2$

$\Rightarrow \frac{0.2588}{a} = \frac{0.3827}{2}$ $implies 0.2588/a=0.3827/2$

$\Rightarrow \frac{0.2588}{a} = 0.19135$ $implies 0.2588/a=0.19135$

$\Rightarrow a = 1.3524$ $implies a=1.3524$ units

Therefore, side $a = 1.3524$ $a=1.3524$ units

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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 $2$ $2$ 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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Explanation:

Explanation:

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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 2 22 and the angle between sides B and C is pi/12π12pi/12, what is the length of side A?

2 Answers

Explanation:

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 $2$ $2$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?