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 $25$ $25$ 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 $25$ $25$ 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 · 2018-06-20T17:40:46

$a = \frac{25}{2} \cdot (\sqrt{3} - 1)$ $a=25/2*(sqrt(3)-1)$

Explanation:

By the Theorem of sines we get

$\frac{sin (\frac{π}{4})}{sin (\frac{π}{12})} = \frac{25}{a}$ $sin(pi/4)/sin(pi/12)=25/a$
solving for $a$ $a$ we get
$a = 25 \cdot \frac{sin (\frac{π}{12})}{sin (\frac{π}{12})}$ $a=25*sin(pi/12)/sin(pi/12)$
so

$a = \frac{25}{2} \cdot (\sqrt{3} - 1)$ $a=25/2*(sqrt(3)-1)$

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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 $25$ $25$ 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 $25$ $25$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?