Question

Given: KL ║ NM , LM = 45, m∠M = 50° KN ⊥ NM , NL ⊥ LM Find: KL
PLEASE HELP IM BEGGING

Answer 1

17.97 units

Explanation:

We are given that KL is parallel to NM and that LM = 45 units and m∠M = 50 degrees. We are also given that KN is perpendicular to NM and that NL is perpendicular to LM.

Using trigonometry, we can find the lengths of NL and KN:

sin(50) = NL/LM

NL = LMsin(50) = 45sin(50) ≈ 34.47

cos(50) = KN/NM

KN = NMcos(50) = 45cos(50) ≈ 34.47

To find KL, we can use the fact that NL is parallel to KL, so we have similar triangles KLN and LMN:

KL/NL = LM/LN

KL/34.47 = 45/cos(50)

KL ≈ 17.97

Therefore, KL is approximately 17.97 units.