Question

A triangle has sides A, B, and C. Sides A and B are of lengths `2` and `1`, respectively, and the angle between A and B is `(5pi)/12`. What is the length of side C?

Answer 1

`color(blue)("As length of side c cannot be negative", color(brown)(c ~~ 2 " units"`

Explanation:

`"Given : " a = 2, b = 1, hatC = (5pi)/12, " To find c"`

As per the Law of Cosines,

`c^2 = a^2 + b^2 - (2 * a * b * cos C)`

`c = +- sqrt(2^2 + 1^2 - (2 * 2* 1 * cos ((5pi)/12))`

`c = +- sqrt(5 - 4 cos ((5pi)/12)) ~~ 2 " units"`

As length of side c cannot be negative, `color(brown)(c ~~ 2 " units"`