In ΔLMN, the measure of ∠N=90°, MN = 6 feet, and NL = 3.5 feet. Find the measure of ∠L to the nearest degree

60 degree

Step-by-step explanation:

If the measure of ∠N = 90°, this shows that ΔLMN is a right angle triangle where

The adjacent side = NL = 3.5 feet

The opposite side = MN = 6 feet, 

To find the measure of ∠L to the, we need to first find the hypothenus side,

So, we will use pythagorean theorem

LM^2 = MN^2 + NL^2

Substitutes MN and NL into the formula

LM^2 = 6^2 + 3.5^2

LM^2 = 36 + 12.25

LM = sqrt(48.25)

LM = 6.9 feet

To Find the measure of ∠L to the nearest degree, let's use trigonometry ratio Soh Cah Toa

SinØ = opposite/hypothenus

Substitute the opposite and hypothenus value into the formula

SinØ = 6/6.9 = 0.86377

Ø = sin^-1(0.86377)

Ø = 59.74 degree

The measure of ∠L to the nearest degree is 60 degrees approximately