Triangle L M N is shown. Angle M L N is a right angle. The length of M L is 5.74, the length of L N is 4, and the length of hypotenuse M N is 7. Law of cosines: a2 = b2 + c2 – 2bccos(A) What is the measure of AngleN to the nearest whole degree? 35° 45° 55° 65°

55⁰

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. There are different types of triangles such as 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, hence:

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

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