Question

The law of cosines states that for any triangle with sides a,b and c and the angle γ opposite the side c,

c² = a²+b²-2ab . cos(γ)

Answer 1

The law of cosines is a mathematical formula used to find the length of a side of a triangle when the lengths of the other two sides and the angle between them are known.

Step-by-step explanation:

The law of cosines is a mathematical formula used to find the length of a side of a triangle when the lengths of the other two sides and the angle between them are known. It states that for any triangle with sides a, b, and c and the angle γ opposite the side c, c² = a² + b² - 2ab * cos(γ).

For example, if you know that side a has a length of 3, side b has a length of 4, and the angle γ opposite side c is 60 degrees, you can use the law of cosines to find the length of side c.

1. Plug the values into the formula: c² = 3² + 4² - 2 * 3 * 4 * cos(60°).
2. Calculate the cosine of 60 degrees: cos(60°) = 0.5.
3. Substitute the values into the formula: c² = 9 + 16 - 24 * 0.5 = 25 - 12 = 13.
4. Take the square root of both sides to find c: c = √13 ≈ 3.605.