How do you solve the right triangle ABC given A = 33°, a = 19, b = 14?

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Answer 1 · 2018-03-27T08:59:49

#color(crimson)("Area of triangle " A_t = (1/2) a b sin C = 111.11 " sq units"#

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

#hat A = 33, a = 19, b = 14#

Applying Law of sines,

#ssin A / a = sin B / b = sin C / c#

#sin B = (b * sin A) / a = (14 * sin 33) / 19 = 0.4013#

#hat B = sin ^ -1 0.4013 = 23.66^@#

#hat C = 180 - 33 - 23.66 = 123.34^@#

#Delta " " A_t = (1/2) a b sin C = (1/2) * 19 * 14 * sin (123.34) = 111.11#