Question

Given: KL ║ NM NM = 52, m∠M = 36° KN ⊥ NM , NL ⊥ LM Find: KN and KL

Answer 1

KN = 24.727 units

KL = 17.966 units

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) =
`(LN)/(NM) = (LN)/(52)`

cos(36) =
`(LM)/(NM) = (LN)/(52)`

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.