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.