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Answer 1 · 2017-11-12T13:44:23

$a = 35, b = 10, c = 29.443$ $a = 35, b = 10, c = 29.443$
$∠ A = 116, ∠ B = 14.88, ∠ C = 49.12$ $/_A = 116, /_B = 14.88, /_C = 49.12$

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

$\frac{35}{{sin 116}^{0} =} \frac{10}{sin B}$ $35 / sin 116^0 = 10 / sin B$

$sin B = \frac{10 \cdot {sin 116}^{0}}{35}$ $sin B = (10 * sin 116^0) / 35$

$∠ B = {14.88}^{0}$ $/_B = 14.88^0$
$∠ C = 180 - 116 - 14.88 = {49.12}^{0}$ $/_C = 180 - 116 - 14.88 = 49.12^0$

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

$c = 10 \cdot (\frac{sin 49.12}{sin 14.88})$ $c = 10*(sin 49.12/ sin 14.88)$

$c = 29.443$ $c = 29.443$

$a = 35, b = 10, c = 29.443$ $a = 35, b = 10, c = 29.443$
$∠ A = 116, ∠ B = 14.88, ∠ C = 49.12$ $/_A = 116, /_B = 14.88, /_C = 49.12$