Question

Find all the missing elements.Round to the nearest tenth.aba = 5b = 2A C = 6BСA = [?]° B =[ 1°C = [ 1°Inter

Answer 1

Step-by-step explanation:

Taking into account the law of cosines, we can write the following equation:

`a^2=b^2+c^2-2bc\cos A`

Then, replacing the values for a, b, and c, we get:

`\begin{gathered} 5^2=2^2+6^2-2(2)(6)\cos A \\ 25=4+36-24\cos A \\ 25=40-24\cos A \end{gathered}`

Solving for cos A, we get:

`\begin{gathered} 25-40=40-24\cos A-40 \\ -15=-24\cos A \\ (-15)/(-24)=(-24\cos A)/(-24) \\ 0.625=\cos A \end{gathered}`

Therefore, the value of angle A is:

`\begin{gathered} \cos ^(-1)(0.625)=A \\ 51.3=A \end{gathered}`

Now, we can use the law of sines, we can write the following equation:

`(\sin B)/(b)=(\sin A)/(a)`

So, replacing the values and solving for B, we get:

`\begin{gathered} (\sin B)/(2)=(\sin 51.3)/(5) \\ \sin B=(\sin 51.3)/(5)*2 \\ \sin B=0.3121 \\ B=\sin ^(-1)(0.3121) \\ B=18.2 \end{gathered}`

In the same way, Angle C is equal to:

`\begin{gathered} (\sin C)/(c)=(\sin A)/(a) \\ (\sin C)/(6)=(\sin 51.3)/(5) \\ \sin C=(\sin51.3)/(5)*6 \\ \sin C=0.9365 \\ C=\sin ^(-1)(0.9365) \\ C=69.5 \end{gathered}`

So, the answers are:

A = 51.3°

B = 18.2°

C = 69.5°