Given the right triangle mlk and pln below ; pl=15, kn=4 and cos(l)= (4/5). find the length of km

We can answer the question above by using the trigonometric functions and the concept of similar triangles. 
Given that cos (L) is 4/5. The length of sides PN and NL can be solved. Please see solution below.
                            4/5 = NL / 15   ;    NL = 12
Solving for PN,
                                 PN² + 12² = 15²
The value of PN is 9.
Then, using the concept of similar triangles,
                                KN/(KN + NL) = PN/ KM
Substituting the known values,
                                 4/(4 + 12) = 9 / KM
The value of KM is 36. 

Idon’t know this and this isn’t middle school work