! ! what is the distance from point n to lm in the figure below?

Step-by-step explanation:

The distance between certain point and a line is measured with a perpendicular line.

So, in this case, the perpendicular line between point N and the line LM is represent by NO, which has a length of 7.5.

Therefore, the distance from point N to LM is 7.5

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

answer: x=3 and y=4

step-by-step explanation: