Respuesta :

Answer:

In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. Using notation as in Fig. 1, the law of cosines states where γ denotes the angle contained between sides of lengths a and b and opposite the side of length c.

Step-by-step explanation:

Answer:

X = 117.9°

Step-by-step explanation:

Rearranging the cosine rule to obtain C

cosC = [tex]\frac{a^2+b^2-c^2}{2ab}[/tex]

Here C = X, a = 50, b = 55, c = 90

cosX = [tex]\frac{50^2+55^2-90^2}{2(50)(55)}[/tex]

        = [tex]\frac{2500+3025-8100}{5500}[/tex]

        = [tex]\frac{-2575}{5500}[/tex], thus

X = [tex]cos^{-1}[/tex]( - [tex]\frac{2575}{5500}[/tex] ≈ 117.9°

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