Given the right triangles MLK and PLN below PL 12 KN 2 and

Given the right triangles MLK and PLN below; PL = 12, KN =2 and cos(L) = 2/3. Find the length of KM.

Soution:

Given that

In above figure
In triangle LNP ( N is a right angle )

therefore

Cos(L) = LN/ PL

LN/12 = 2/3 ( Given in question Cos(L) =2/3 and PL = 12

LN = 12 * (2/3) = 8

LN = 8

Now again in triangle LKM which right angled at K

LK = LN +NK

LK = LN + NK = 8 +2 = 10 ( Given NK = 2 and LN = 8 as per our last calculation)

LK = 10

Again in triangle LKM

Sin (L) = ( 1– Cos²(L) = (1-(2/3)²) = (5/9) = 5/3

and tan (L) = sin (L) /Cos(L) =KM/LK = (5/3)/(2/3)

KM / 10 = 5/2

KM = 55

Answer