Question

A triangle has sides A, B, and C. Sides A and B are of lengths `4` and `3`, respectively, and the angle between A and B is `(5pi)/6`. What is the length of side C?

Answer 1

≈ 2.05

Explanation:

In this triangle 2 sides and the angle between them are known , hence use the ' cosine rule '.

for this triangle the cosine rule is :

`C^2 = A^2 + B^2 - ( 2ABcos((5pi)/6))`

hence `C^2 = 4^2 + 3^2 - ( 2 xx 4 xx 3 xxcos((5pi)/6))`

`C^2 = 16 + 9 - (24cos((5pi)/6))`

= 25 - 20.78 = 4.22

now `C^2 = 4.22 rArr C = sqrt4.22 ≈ 2.05`