Question

two triangles can be formed with the given information use the law of sines to solve the triangle. B=46 a=12 b=11

Answer 1

We will have the following:

First, we sketch:

Now, we will determine the missing information, that is.

`\begin{gathered} (sin(A))/(12)=(sin(46))/(11)\Rightarrow sin(A)=(12sin(46))/(11) \\ \\ \Rightarrow A=sin^(-1)((12sin(46))/(11))\Rightarrow A\approx51.7 \end{gathered}`

Now, we determine the missing angle:

`\begin{gathered} A+B+C=180\Rightarrow51.7+46+C=180 \\ \\ \Rightarrow C\approx82.3 \end{gathered}`

Now, we determine the missing side:

`\begin{gathered} (c)/(sin(82.3))=(11)/(sin(46))\Rightarrow c=(11sin(82.3))/(sin(46)) \\ \\ \Rightarrow c\approx15.2 \end{gathered}`

So, the missing information is:

A = 51.7°, C = 82.3° & c = 15.2