The measure of the angle N is 55 degrees.
A triangle is a polygon with three sides and three angles.
There are different types of triangles such as the isosceles triangle, equilateral triangle, scalene triangle, right-angled triangle.
The law of cosines states that for a triangle with sides a, b, and c and the corresponding angles opposite to the sides which are A, B, and C. Then:
a² = b² + c² – 2bccos(A)
Let ML = a = 5.74, LN = b = 4, MN = c = 7.
∠N is opposite to side ML. Let ∠N be A,
a² = b² + c² – 2bccos(A)
2bc* cos(A) = b² + c² – a²
Substituting:
2(4)(7) × cos(A)= 4² + 7² - 5.74²
56cos(A) = 32.0524
cos(A) = 0.5723
A = cos⁻¹(0.5723)
A = 55⁰
A = ∠N = 55⁰
Hence, the measure of the angle N is 55 degrees.
To know more about the Law of Cosine click the link given below.
https://brainly.com/question/17189723
