I dont understand this triangle math question

If its not too much trouble

The Directions said: two triangles can be formed using the given measurements. Solve both triangles.

A= 60 degrees, side a = 12, side b = 13

I drew the triangle, found all sides and angles, but i dont get how "two triangles can be formed" (i cant visualize it, because i dont know how to draw it with 2 triangles?)

1 Attachment(s)

Triangles: the Ambiguous Case

Hello yeunju Quote:

Originally Posted by

**yeunju** If its not too much trouble

The Directions said: two triangles can be formed using the given measurements. Solve both triangles.

A= 60 degrees, side a = 12, side b = 13

I drew the triangle, found all sides and angles, but i dont get how "two triangles can be formed" (i cant visualize it, because i dont know how to draw it with 2 triangles?)

A question like this, where you are given two sides of a triangle and the non-included angle, and two triangles are possible, is called the **Ambiguous Case**. The attached diagram shows how you can draw the two triangles with the measurements you were given.

You've probably found the one where $\displaystyle \angle B$ is acute (that's $\displaystyle B_2$ in my diagram). But there's also a possibility that $\displaystyle \angle B$ is obtuse (like $\displaystyle B_1$). Since $\displaystyle \triangle B_1CB_2$ is isosceles, you can probably see why $\displaystyle \angle AB_1C = 180^o - \angle AB_2C$.

Can you complete the solution of the second triangle now?

Grandad