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 $12$ $12$ 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 $12$ $12$ 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 · 2016-09-30T19:02:16

$a \approx 4.39$ $a ~~ 4.39$

Explanation:

Using the notation where the sides are the lowercase letters, a, b, and c and the opposite angles are the uppercase letters, A, B, and C. The law of sines is:

$\frac{a}{sin (A)} = \frac{b}{sin (B)} = \frac{c}{sin (C)}$ $a/sin(A) = b/sin(B) = c/sin(C)$

We are given:
$c = 12, C = \frac{π}{4} and A = \frac{π}{12}$ $c = 12, C = pi/4 and A = pi/12$

Using the first and last part of the law of sines:

$\frac{a}{sin (A)} = \frac{c}{sin (C)}$ $a/sin(A) = c/sin(C)$

$a = \frac{12 sin (\frac{π}{2})}{sin (\frac{π}{4})}$ $a = (12sin(pi/2))/sin(pi/4)$

$a \approx 4.39$ $a ~~ 4.39$

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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 $12$ $12$ 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/4π4pi/4. If side C has a length of 12 1212 and the angle between sides B and C is pi/12π12pi/12, what is the length of side A?

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Explanation:

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