A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{3}$ $(pi)/3$ . If side C has a length of $16$ $16$ and the angle between sides B and C is $\frac{3 π}{8}$ $( 3 pi)/8$ , 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 $\frac{π}{3}$ $(pi)/3$ . If side C has a length of $16$ $16$ and the angle between sides B and C is $\frac{3 π}{8}$ $( 3 pi)/8$ , what are the lengths of sides A and B?

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Answer 1 · 2018-03-26T02:43:16

$length of side a = \frac{c \cdot sin A}{sin C} = 17.07$ $color(green)("length of side " a) = (c * sin A) / sin C = color(green)(17.07)$

$Length of side b = \frac{c \cdot sin B}{sin C} = 2.41$ $color(green)("Length of side " b) = (c * sin B) / sin C = color(green)(2.41)$

Explanation:

$Given : ˆ C = \frac{π}{3}, c = 16, ˆ A = \frac{3 π}{8}$ $"Given : " hat C = pi/3, c = 16, hat A = (3pi) / 8$

$To find lengths of sides a & b$ $"To find lengths of sides a & b"$

![http://www.dummies.com/education/math/trigonometry/laws-of-sines-and-cosines/]( useruploads.socratic.org )

$ˆ B = π - \frac{π}{3} - \frac{5 π}{8} = \frac{π}{24}$ $hat B = pi - pi/3 - (5pi)/8 = pi/24$

Applying Law of sines,

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

$a = \frac{c \cdot sin A}{sin C} = \frac{16 \cdot sin (\frac{3 π}{8})}{sin (\frac{π}{3})} = 17.07$ $color(green)(a) = (c * sin A) / sin C = (16 * sin ((3pi)/8)) / sin(pi/3) = color(green)(17.07)$

$b = \frac{c \cdot sin B}{sin C} = \frac{16 \cdot sin (\frac{π}{24})}{sin (\frac{π}{3})} = 2.41$ $color(green)(b) = (c * sin B) / sin C = (16 * sin (pi/24)) / sin(pi/3) = color(green)(2.41)$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{3}$ $(pi)/3$ . If side C has a length of $16$ $16$ and the angle between sides B and C is $\frac{3 π}{8}$ $( 3 pi)/8$ , 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 (pi)/3π3(pi)/3. If side C has a length of 16 1616 and the angle between sides B and C is ( 3 pi)/83π8( 3 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 $\frac{π}{3}$ $(pi)/3$ . If side C has a length of $16$ $16$ and the angle between sides B and C is $\frac{3 π}{8}$ $( 3 pi)/8$ , what are the lengths of sides A and B?