Question

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

Answer 1

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

Explanation:

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`