Question 453477
If we draw a height (h) from vertex M it forms two right triangles LNM and KNM where N is a point where height h intersects KL.
:
It also divides KL into two pieces x=KN and y=LN:
{{{x+y=7}}} -> x=7-y
:
Knowing that angle L=30 and angle M=110, it makes angle K=40.
Now we have:
{{{tan(30)=h/y}}} -> h=tan(30)*y
{{{tan(40)=h/x}}} -> h=tan(40)*x
:
{{{tan(40)*x=tan(30)*y}}}, substitute x with 7-y
{{{tan(40)*(7-y)=tan(30)*y}}}
{{{tan(40)*7-tan(40)*y=tan(30)*y}}}
{{{y=7*tan(40)/(tan(30)+tan(40))}}}
y=4.1
:
x=7-y -> x=7-4.1 -> x=2.9
:
We can find KM knowing that:
{{{cos(40)=x/KM}}}
{{{KM=x/cos(40)}}}
KM=3.8