Question

A triangle has sides A, B, and C. Sides A and B are of lengths `3` and `2`, respectively, and the angle between A and B is `(5pi)/12`. What is the length of side C?

Answer 1

C ≈ 3.15

Explanation:

In this triangle , 2 sides and the angle between them are known.In this situation to solve for C use `color(blue)(" cosine rule ")`

for this triangle the cosine rule is

`C^2 = A^2 + B^2 - (2ABcostheta)`

here A = 3 , B = 2 and `theta = (5pi)/12`
substitute these values into formula

`C^2 = 3^2 + 2^2 - ( 2 xx 3 xx2cos((5pi)/12 )`

= 9+4 - 3.1 = 13 - 3.1 = 9.9

`C^2 = 9.9 rArr C = sqrt9.9 ≈ 3.15`