To find the length of LN in a circle M, we can use the Law of Cosines to solve for the unknown side length. By using the given angle measure and the known side length, we can substitute into the formula and calculate the value of LN. The length of LN is approximately 26.48 units.
To find the length of LN in circle M, we can use the fact that the sum of the angles in a triangle is 180 degrees. We are given that angle LMN is 126 degrees, so angle MLN must be 180 - 126 = 54 degrees.
We can now use the Law of Cosines to find the length of LN: LN^2 = LM^2 + MN^2 - 2(LM)(MN)cos(MLN). Substituting the known values, we get: LN^2 = 17^2 + MN^2 - 2(17)(MN)cos(54).
Finishing the calculation, we can solve for LN using algebraic steps and rounding to the nearest hundredth. The final result is LN ≈ 26.48 units.