Question

Using the law of cosines, what is m<X 61, 79, 82, 91

Answer 1

Answer: 79°


Explanation:


1) Law of cosines:


In a triangle with sides a, b, c whose opposite angles are, respectively, A, B and C, the law of cosines states:

c² = a² + b² - 2 a×b×cos (C)

2) In the triangle of the figure you have

c = 9
C = X
a = 6
b = 8
⇒ 9² = 6² + 8² - 2(6)(8) cos(X)
⇒ 81 = 36 + 64 - 96cos(X)
⇒ 96cos(X) = 36 + 64 - 81 = 19
⇒ cos(X) = 19 / 96 
⇒ X = arccos(19/26) = 78.6° ≈ 79°