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 answers to 3 decimals

Answer 1

Place M at the origin and LM along the x-axis, so L = (45,0). The ray MN makes a 50° angle with LM, so points on MN have coordinates (t cos50°, t sin50°). N also lies on the vertical through L (NL ⟂ LM), so N = (45, 45 tan50°).

KL is parallel to MN, so the line KL through L has direction (cos50°, sin50°). KN is perpendicular to MN, so the line through N perpendicular to MN has direction (-sin50°, cos50°). Solving for their intersection K gives KL = s = 45 * sin^2(50°) / cos(50°) and KN = 45 * sin(50°).

Numerical values (rounded to 3 decimals):
- KN = 45·sin(50°) ≈ 34.472
- KL = 45·sin^2(50°)/cos(50°) ≈ 41.024