1: The question: The area of triangle ABC is 24√3, side a = 6, and side b = 16. The value of angle C is
(B) 30° or 150°
(D) 60° or 120°
(E) None of the above
The book says the answer is D, but how do you know for certain that you can form 2 triangles? I tried using the a>h, a less than b method to see if there are two triangles but I can't because this isn't even a SSA problem. I get that when you use the area formula for a triangle, you get two answers for angle C: (1/2)*16*6sin(θ)=24√3 gets you θ=60° and 120°, but why can't answer (C) be correct? Couldn't there be only one triangle and thus you can only have one value for angle C?