Question

Law of Cosine/Sine problem.

Answer 1

`\displaystyle 12,766277792...`

Step-by-step explanation:

Solving for Angles

`\displaystyle \frac{sin\angle{C}}{c} = \frac{sin\angle{B}}{b} = \frac{sin\angle{A}}{a}`

Do not forget to use
`\displaystyle arcsin` or
`\displaystyle sin^(-1)`towards the end, or the result will be thrown off.

Solving for Edges

`\displaystyle \frac{c}{sin\angle{C}} = \frac{b}{sin\angle{B}} = \frac{a}{sin\angle{A}}`

Well, let us get to work:

`\displaystyle (18)/(sin\:115) = (c)/(sin\:40) \hookrightarrow (18sin\:40)/(sin\:115) = c \\ \\ \boxed{12,766277792... = c}`

I am joyous to assist you at any time.

Answer 2

Either or can be used with any triangle...I personally find the law of sines is often more compact as in this case we can just say;

(sin115)/18=(sin40)/c (with no need for b or B as would be needed with the law of cosines...)

c=18(sin40)/(sin115)

c≈12.77