Given: KL ║ NM, LM = 45, m∠M = 50° KN⊥NM, NL ⊥ LM

Question

Find: KN and KL

So I drew it found that m∠K=90°, m∠LNM=40°, m∠KNL=50°
using the rules of trigonometry, I got:
(NL/45) =tan(50°) and that NL=53.63
I checked it and it was correct so using that I plugged it in as a hyp.: (KN/63.63) =cos(50°), KN=34.47 and when I checked that, it was also correct. So I thought I was on a roll so I pluged in 34.37 as an adj. side: (KL/34.47)=tan(50°) and got KL=41.08. And guess what,it was wrong. ughh. I tried the pythagoren th. instead and got 41.09 (from rounding) and it was still wrong. I got 52.52 once and it was also wrong.

Answer 1

If you did what you typed, I'm not surprised. It should have been

(KN/53.63) = cos(50°)

Answer 2

Its KL = 41.082