Answer:
[tex]\displaystyle 33,8 ≈ b \\ 55,1 ≈ a \\ 35° = m∠B[/tex]
Step-by-step explanation:
We will be using the Law of Sines to find edges b and a one at a time, therefore we will use the given variables in the formulas:
Solving for Angles:
[tex]\displaystyle \frac{sin∠C}{c} = \frac{sin∠B}{b} = \frac{sin∠A}{a}[/tex]
**Use [tex]\displaystyle arcsin\:or\:sin^{-1}[/tex]in your solution or you will throw the result off!
Solving for Edges:
[tex]\displaystyle \frac{c}{sin∠C} = \frac{b}{sin∠B} = \frac{a}{sin∠A}[/tex]
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[tex]\displaystyle \frac{33}{sin\:34} = \frac{b}{sin\:35} \hookrightarrow \frac{33sin\:35}{sin\:34} = b \hookrightarrow 33,848824408... = b \\ \\ 33,8 ≈ b[/tex]
We will now define edge a:
[tex]\displaystyle \frac{33}{sin\:34} = \frac{a}{sin\:111} \hookrightarrow \frac{33sin\:111}{sin\:34} = a \hookrightarrow 55,093964682... = a \\ \\ 55,1 ≈ a[/tex]
This triangle is now deemed solved.
***The fact that you solved for the [tex]\displaystyle m∠B[/tex]tells me that you understood what to when it comes to the interior angles of triangles, so I did not have to cover that. Good wourk citisen!
I am delighted to assist you at any time. If you have further questions though, comment them and I will do my very best to answer them.
