SOLUTION: In the triangle KLM the length of KM is approximately what?: (Round to the nearest tenth) KL= 7in Angle M= 110 degrees Angle L=30 degrees

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Question 453477: In the triangle KLM the length of KM is approximately what?: (Round to the nearest tenth)
KL= 7in
Angle M= 110 degrees
Angle L=30 degrees
Answer by pedjajov(51) About Me  (Show Source):
You can put this solution on YOUR website!
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%2By=7 -> x=7-y
:
Knowing that angle L=30 and angle M=110, it makes angle K=40.
Now we have:
tan%2830%29=h%2Fy -> h=tan(30)*y
tan%2840%29=h%2Fx -> h=tan(40)*x
:
tan%2840%29%2Ax=tan%2830%29%2Ay, substitute x with 7-y
tan%2840%29%2A%287-y%29=tan%2830%29%2Ay
tan%2840%29%2A7-tan%2840%29%2Ay=tan%2830%29%2Ay
y=7%2Atan%2840%29%2F%28tan%2830%29%2Btan%2840%29%29
y=4.1
:
x=7-y -> x=7-4.1 -> x=2.9
:
We can find KM knowing that:
cos%2840%29=x%2FKM
KM=x%2Fcos%2840%29
KM=3.8