Raymond J. answered • 12/11/20
Patient with Ability to Explain in Many Ways
When you draw this out you end up with a trapezoid KLMN. NL divides it into two triangles. M has angle of 50° and angle MLN has angle 90° (because NL is ⊥ to ML). From there you can figure out all the angles. Angle LNM is 40° as is angle KLN. Angle LNK is also 50°
From there use the trigonometric functions to determine the lengths of the other sides. You're given LM = 45. Since you need to find KL and KN, you need to find NL. To find NL we need the hypotenuse of triangle NLM (which is NM) first. From cos(θ) = adj/hyp we have cos(50) = 45/NM, or NM = 70. From there we determine NL from sin(50) = NL/70 or NL = 70*sin(50) = 53.6.
The rest is simply using the trigonometric functions to determine KL and KN. Good Luck!
