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 $23$ $23$ 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 · 2018-05-24T04:24:29

Lengths of sides $a = 42.5, b = 28$ $color(brown)(a = 42.5, b = 28$

$ˆ A = \frac{5 π}{8}, ˆ C = \frac{π}{6}, c = 23$ $hat A = (5pi)/8, hat C = pi/6, c = 23$

To find $a, b$ $a, b$

As per Law of Sines,

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

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

$a = \frac{23 \cdot sin (\frac{5 π}{8})}{sin (\frac{π}{6})} = 42.5$ $a = (23 * sin ((5pi)/8)) / sin (pi/6) = 42.5$

$b = \frac{23 \cdot sin (5 \frac{π}{24})}{sin (\frac{π}{6})} = 28$ $b = (23 * sin (5pi/24) )/ sin (pi/6) = 28$

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 2323 and the angle between sides B and C is 5π8( 5 pi)/8, what are the lengths of sides A and B?