Answer:
The ratio is [tex]\frac{CL}{AC}=\frac{2BC}{3AB}[/tex]
Step-by-step explanation:
we know that
In the right triangle ABC
[tex]cos(30\°)=AC/AB[/tex]
[tex]AC=cos(30\°)(AB)[/tex]
we know that
[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]
substitute
[tex]AC=\frac{\sqrt{3}}{2}(AB)[/tex]
In the right triangle LBC
[tex]tan(30\°)=CL/BC[/tex]
[tex]CL=tan(30\°)(BC)[/tex]
we know that
[tex]tan(30\°)=\frac{\sqrt{3}}{3}[/tex]
substitute
[tex]CL=\frac{\sqrt{3}}{3}(BC)[/tex]
see the attached figure to better understand the problem
Find the ratio CL: AC
we have
[tex]CL=\frac{\sqrt{3}}{3}(BC)[/tex]
[tex]AC=\frac{\sqrt{3}}{2}(AB)[/tex]
[tex]\frac{CL}{AC}=\frac{\frac{\sqrt{3}}{3}(BC)}{\frac{\sqrt{3}}{2}(AB)}=\frac{2BC}{3AB}[/tex]
