Question

Using the law of cosines, a=2.2

Answer 1

Answer: 81°


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:


b² = a² + c² - 2 (a)(c) cos (B)


2) In the triangle of the figure you have


b = 4.0
B = ?
a = 2.2
c = 3.7

⇒ (4.0)² = (2.2)² + (3.7)² - 2 (2.2) (3.7) cos(B)

⇒ 16 = 4.84 + 13.69 - 16.28cos(B)

⇒ 16.28 cos(B) = 4.84 + 13.69 - 16 = 2.53

⇒ cos(B) = 2.53 / 16.28

⇒ X = arccos(2.53 / 16.28 ) = 81.06° ≈ 81°