How do you solve the $triangle ABC$ given $C=84^circ, c=7, a=2$ ?

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Answer 1 · 2018-02-24T13:07:01

$a = 2, b = 6.92, c = 7$

$hatA = 16.5^@, hatB = 79.5^@, hatC = 84^@$

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Given : $hatC = 84^@, a = 2, c = 7$

Applying law of sines,

$sin A / a = sin C / c$

$sin A = (a sin C) / sin A = (2 * sin 84) //7 = 0.2841$

$hatA = sin ^-1 (0.2841) ~~ 16.5^@$

Sum of the three angles of a triangle equals $180^@$

Hence $hatB = 180 - 84 - 16.5 = 79.5^@$

$b = (c sin B) / sin C = (7 * sin 79.5) / sin 84 = 6.92$

How do you solve the triangle ABCtriangle ABC given C=84^circ, c=7, a=2C=84^circ, c=7, a=2?