Answer:
JK - 20
Step-by-step explanation:
As JLM is a square triangle, so that we have the formula to calculate the corner ∡LMJ
We have tan∡LMJ = LJ/ JM =45/60 = 0.75
+) As ∡LMK = ∡KMJ => tan ∡LMK = tan ∡KMJ
+) ∡LMK + ∡KMJ = ∡LMJ
We have the formula: tan (x+y) = [tex]\frac{tan x + tan y}{1 - tanx* tany}[/tex]
=> tan (∡LMK + ∡KMJ) = [tex]\frac{tanLMK + tan KMJ}{1- tanLMK*tanKMJ} = \frac{2 tan KMJ}{1-tan^{2}KMJ }[/tex]
As tan (∡LMK + ∡KMJ) = tan ∡LMJ = 0.75
=> [tex]\frac{2 tan KMJ}{1-tan^{2}KMJ }[/tex] = 0.8
=> 0.75 - 0.75 x [tex]tan^{2} KMJ[/tex] = 2tanKMJ
As 0 < ∡KMJ < [tex]\pi /2[/tex] => tan KMJ > 0
=> tan KMJ = 1/3
As JKM is also a square triangle
=> We have tan∡KMJ = JK/JM
=> 1/3 = JK/JM
=. JK = JM x (1/3) = 60 x (1/3) = 20
So JK = 20
