How do you solve the triangle given A= 38 degrees B=57 degrees and c=27?

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Answer 1 · 2018-03-26T02:53:44

$color(blue)(hat C = 85^@, a = 16.69., b = 22.73$

$color(brown)("Area of triangle " A_t = (1/2) b c sin A = 188.92 " sq units"$

$hat A = 38^@, hat B = 57^@, c = 27$

$" To solve the triangle"$

$hat C = 180 = hat A - hat B = 180 - 38 - 57 = 85^@$

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

Applying Law of sines,

$a / sin A = b / sin B = c / sin C$

$a = (c sin A) / sin C = (27 * sin 38) / sin 85 = 16.69$

$b = (c sin B) / sin C = (27 * sin 57) / sin 85 = 22.73$

$"Area of triangle " A_t = (1/2) b c sin A = (1/2) 22.73 * 27 * sin 38 = 188.92 " sq units"$