Question

Please Help! Due tonight! Solve the triangle. Round to nearest tenth, if necessary.

Answer 1

`\displaystyle 33,8 ≈ b \\ 55,1 ≈ a \\ 35° = m∠B`

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:

`\displaystyle (sin∠C)/(c) = (sin∠B)/(b) = (sin∠A)/(a)`

**Use
`\displaystyle arcsin\:or\:sin^(-1)`in your solution or you will throw the result off!

Solving for Edges:

`\displaystyle (c)/(sin∠C) = (b)/(sin∠B) = (a)/(sin∠A)`

__________________________________________________________

`\displaystyle (33)/(sin\:34) = (b)/(sin\:35) \hookrightarrow (33sin\:35)/(sin\:34) = b \hookrightarrow 33,848824408... = b \\ \\ 33,8 ≈ b`

We will now define edge a:

`\displaystyle (33)/(sin\:34) = (a)/(sin\:111) \hookrightarrow (33sin\:111)/(sin\:34) = a \hookrightarrow 55,093964682... = a \\ \\ 55,1 ≈ a`

This triangle is now deemed solved.

***The fact that you solved for the
`\displaystyle m∠B`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.