Question

A triangle has sides A, B, and C. Sides A and B are of lengths `5` and `8`, respectively, and the angle between A and B is `(11pi)/12`. What is the length of side C?

Answer 1

`color(indigo)("Length of side c " = sqrt(a^2 + b^2 - (2 a b cos C)) ~~ 12.89`

Explanation:

`Given : a = 5, b = 8, hat C = (11pi)/12, "To find side c"`.

Applying cosine law,

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

`c = sqrt(5^2 n+ 8^2 - (2 * 5 * 8 * cos ((11pi)/12)`

`color(indigo)("Length of side c " = sqrt(25 + 64 - 80 cos ((11pi)/12)) ~~ 12.89`