How do you solve the triangle given A=47, a=67, b=83?

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Answer 1 · 2018-05-24T04:54:24

#color(purple)(hat A = 34.42^@, hat B = 53.84^@, hat C = 91.74^@#

#a = 47, b = 67, c = 83#

As per Law of Cosines,

#a^2 = b^2 + c^2 - 2 b c cos A#

#cos A = (b^2 + c^2- a^2) / (2bc)#

#cos A = (67^2 + 83^2 - 47^2) / (2 * 67 * 83)#

#cos A = 0.8244#

#hat A = cos ^-1 0.8244 = 34.42^@#

Similarly, #cos C = (b^2 + a^2- c^2) / (2ab)#

#cos C = (47^2 + 67^2 - 83^2) / (2 * 47 * 67)#

#cos C = -0.0303#

#hat C = 91.74^@#

#hat B = 180 - hat A - hat C#

#hat B = 180 - 34.42 - 91.74 = 53.84^@#