Question

find the indicated lengths: given KL parallel NM and LM=45, the measure of angle M=50 degrees, and KN perpindicular NM. and NL perpindicular LM find KN and KL. round the answer to 3 decimals

Answer 1

Place L at (0,0), M at (45,0). Since NL ⟂ LM, let N = (0, t). Angle M = 50° in triangle MNL gives tan 50° = t/45, so t = 45 tan 50°.

With NM = (45, -t) and KL ∥ NM, KL is along that direction and K is the point on that line for which KN ⟂ NM. Working out the distances (or using trig) gives
- KN = 45 sin 50°
- KL = 45 sin 50° · tan 50°.

Compute numerically:
- KN = 45·sin(50°) ≈ 34.472
- KL = 45·sin(50°)·tan(50°) ≈ 41.024

Answers to three decimals: KN ≈ 34.472, KL ≈ 41.024.