Question

Suppose a triangle has sides a, b, and c let theta be the angle opposite the side of length a. If cos theta < 0 what must be true? a- b^2+c^2>a^2. b- a^2+b^2=c^2. c- b^2+c^2c^2

Answer 1

The answer is

b^2 + c^2 < a^2

Answer 2

Using the cosine rule, a² =  b² +  c² -2 bc cos θSImplifying the equation in terms of cos  theta,
cos(θ) = (a² + c² - b²)/(2bc) 
(a² + c² - b²)/(2bc) > 0 a² + c² - b² > 0 
assuming b and c are non zeros, the resulting inequality should be
a² + c² > b²

THe appicable inequality is a