The problem is as follows:
The figure from below shows a certain terrain has the shape of a triangle $\triangle ABC$ which is obtuse on $B$. Assuming the line connecting $AM$ is a bisector whose angle is $\beta$ and $\angle ACB=20^{\circ}$ and $\angle ABC= 120^{\circ}$ and $\angle CMA=90^{\circ}$ and $CM=8\sqrt{3}\,m$. Find the cost of placing a fence on $CM$ if the owner of the terrain consulted with the hardware store and the price is $\$3.0$ per meter.
The alternatives in my book are as follows:
$\begin{array}{ll} 1.&\$\,21.00\\ 2.&\$\,24.00\\ 3.&\$\,48.00\\ 4.&\$\,32.00\\ \end{array}$
In my attempt to solve this problem the only thing which I was able to spot is that the bisector angle is $\beta= 20^{\circ}$.
This comes because of the sum of the interior angles in the triangle add up to $180^{\circ}$.
Hence on $\triangle ABC$:
$2\beta+120+20=180$
$\beta= 20^{\circ}$
Then I could also spot is that the small right triangle has the interior angles of 40^{\circ} and 50^\circ because by interior and exterior angle on the smaller triangle. But other than that I cannot spot something else.
Can someone help me?. I think in this problem is required congruence or similarity but I don't know how to use those here.
Please an answer must include a drawing Since it is not easy for me to spot the relationships and construction that would help me better to understand what's going on.
