How do you solve the triangle given A=56, B=22, a=12.2?

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Answer 1 · 2018-03-25T04:53:23

$hat C = 102, b = 5.42, c = 14.39$

$color(brown)("Perimeter of the triangle " = P = 32.01 " units"$

$color(purple)("Area of the triangle " A_t ~~ 32.34 " sq units"$

Given : $hat A = 56, hat B = 22, a = 12.2$

$hat C = 180 - (hat A + hat B) = 180 - 56 - 22 = 102$

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Applying Law of Sines,

$12.2 / sin 56 = b / sin 22 = c / sin 102$

$b = (12 * sin 22) / sin (56) ~~ 5.42$

$c = (12.2 * sin 102) / sin 56 ~~ 14.39$

$color(brown)("Perimeter of the triangle " = P = 12.2 + 5.42 + 14.39 = 32.01 " units"$

$color(purple)("Area of the triangle " A_t = (1/2) a b sin C = (1/2) 12.2 * 5.42 * sin 102 ~~ 32.34 " sq units"$