Given α = 30◦ and b = 10, choose four different values for a so that: (a) the information yields no triangle

(b) the information yields exactly one right triangle

(c) the information yields two distinct triangles

(d) the information yields exactly one obtuse triangle

Please explain/show work.

c

Step-by-step explanation:

An obtuse triangle is a triangle in which one of the angles is an obtuse angle. (Obviously, only a single angle in a triangle can be obtuse or it wouldn't be a triangle.) A triangle must be either obtuse, acute, or right. From the law of cosines, for a triangle with side lengths , , and , (1)

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8