A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{6}$ $(pi)/6$ . If side C has a length of $2$ $2$ and the angle between sides B and C is $\frac{5 π}{8}$ $( 5 pi)/8$ , what are the lengths of sides A and B?

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{6}$ $(pi)/6$ . If side C has a length of $2$ $2$ and the angle between sides B and C is $\frac{5 π}{8}$ $( 5 pi)/8$ , what are the lengths of sides A and B?

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Answer 1 · 2018-02-18T16:19:28

Length of side $a = 3.6955, b = 2.435$ $color(blue)(a = 3.6955, b = 2.435)$

Explanation:

$ˆ C = \frac{π}{6}, ˆ A = \frac{5 π}{8}, c = 2$ $hatC = pi/6, hatA = (5pi)/8, c = 2$

To find sides a, b

$ˆ B = π - \frac{5 π}{8} - \frac{π}{6} = \frac{5 π}{24}$ $hatB = pi - (5pi)/8 - pi/6 = (5pi)/24$

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

$a = \frac{c sin A}{sin C} = \frac{2 sin (\frac{5 π}{8})}{sin (\frac{π}{6})} = 3.6955$ $a = (c sin A) / sin C = (2 sin ((5pi)/8)) / sin (pi/6) = 3.6955$

$b = \frac{c sin B}{sin C} = \frac{2 \cdot sin (\frac{5 π}{24})}{sin (\frac{π}{6})} = 2.435$ $b = (c sin B) / sin C= (2 * sin ((5pi)/24) ) / sin (pi/6) = 2.435$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{6}$ $(pi)/6$ . If side C has a length of $2$ $2$ and the angle between sides B and C is $\frac{5 π}{8}$ $( 5 pi)/8$ , what are the lengths of sides A and B?

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A triangle has sides A, B, and C. The angle between sides A and B is π6(pi)/6. If side C has a length of 22 and the angle between sides B and C is 5π8( 5 pi)/8, what are the lengths of sides A and B?

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{6}$ $(pi)/6$ . If side C has a length of $2$ $2$ and the angle between sides B and C is $\frac{5 π}{8}$ $( 5 pi)/8$ , what are the lengths of sides A and B?