Question

Calculate JK if LJ=45, JM=60 and LM=75

Answer 1

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) = $\frac{tan x + tan y}{1 - tanx* tany}$

=> tan (∡LMK + ∡KMJ) = $\frac{tanLMK + tan KMJ}{1- tanLMK*tanKMJ} = \frac{2 tan KMJ}{1-tan^{2}KMJ }$

As tan (∡LMK + ∡KMJ) = tan ∡LMJ  = 0.75

=> $\frac{2 tan KMJ}{1-tan^{2}KMJ }$ = 0.8

=> 0.75 - 0.75 x $tan^{2} KMJ$ = 2tanKMJ

As 0 <  ∡KMJ  < $\pi /2$ => 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