Question

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

Answer 1

Answer:

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

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:

$\displaystyle \frac{sin∠C}{c} = \frac{sin∠B}{b} = \frac{sin∠A}{a}$

**Use $\displaystyle arcsin\:or\:sin^{-1}$in your solution or you will throw the result off!

Solving for Edges:

$\displaystyle \frac{c}{sin∠C} = \frac{b}{sin∠B} = \frac{a}{sin∠A}$

__________________________________________________________

$\displaystyle \frac{33}{sin\:34} = \frac{b}{sin\:35} \hookrightarrow \frac{33sin\:35}{sin\:34} = b \hookrightarrow 33,848824408... = b \\ \\ 33,8 ≈ b$

We will now define edge a:

$\displaystyle \frac{33}{sin\:34} = \frac{a}{sin\:111} \hookrightarrow \frac{33sin\:111}{sin\:34} = a \hookrightarrow 55,093964682... = a \\ \\ 55,1 ≈ a$

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.