How do you solve the triangle given $A=102.4^circ, C=16.7^circ, a=21.6$ ?

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Answer 1 · 2017-12-31T11:53:01

$B = 60.9^circ$
$c approx 6.4$
$b approx 19.3$

Since the angles must sum to $180^circ$ , we know that:

$B = 180^circ-102.4^circ-16.7^circ = 60.9^circ$

We know that $c/sin(C) = a/sin(A)\rightarrow c=(a*sin(C))/sin(A)$ .

Substituting we have $c = (21.6*sin(16.7^circ))/sin(102.4^circ) approx 6.4$

Similarly $b/sin(B) = a/sin(A)\rightarrow b=(a*sin(B))/sin(A)$ .

Substituting we have $b = (21.6*sin(60.9^circ))/sin(102.4^circ) approx 19.3$

How do you solve the triangle given A=102.4^circ, C=16.7^circ, a=21.6A=102.4^circ, C=16.7^circ, a=21.6?