Answer:
KN = 24.727 units
KL = 17.966 units
Step-by-step explanation:
It is given that NM = 52 units and m∠M=36 degrees.
The triangle LMN in right angled triangle. By using trigonometry,
sin(36) = [tex]\frac{LN}{NM} = \frac{LN}{52}[/tex]
cos(36) = [tex]\frac{LM}{NM} = \frac{LN}{52}[/tex]
Thus, LN = 52(sin(36)) and LM = 52(cos(36))
Construct a line from L to MN , which is perpendicular to NM, and the point on NM be point A.
In triangle LMA, LA = (LM)(sin(36)). Further, as rectangle KNAL is formed,
LA = KN = (LM)(sin(36)) = (52)(sin(36))(cos(36)) = 24.727 units.
In triangle LAN, AN = (LN)(cos(54)). As rectangle KNAL,
KL = AN =(LN)(cos(54)) = (52)(sin(36))(cos(54)) = 17.966 units.
