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 $1$ $1$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?

Question

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 $1$ $1$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?

1 Answer

Impact of this question

1353 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-05T08:27:22

$a = 0.2679$ $a=0.2679$ units

Explanation:

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

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

It is given that side $c = 1 .$ $c=1.$

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

$\Rightarrow \frac{sin (\frac{π}{12})}{a} = \frac{sin (\frac{7 π}{12})}{1}$ $implies Sin(pi/12)/a=sin((7pi)/12)/1$

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

$\Rightarrow a = \frac{0.2588}{0.9659} = 0.2679$ $implies a=0.2588/0.9659=0.2679$

$\Rightarrow a = 0.2679$ $implies a=0.2679$ units

Therefore, side $a = 0.2679$ $a=0.2679$ units

Science

Math

Humanities

... and beyond

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 $1$ $1$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A triangle has sides A, B, and C. The angle between sides A and B is 7π12(7pi)/12. If side C has a length of 11 and the angle between sides B and C is π12pi/12, what is the length of side A?

1 Answer

Explanation:

Related questions

Impact of this question

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 $1$ $1$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?