Solving two triangles inside one triangle?

[yeunju]

So, two triangles can be formed using the given measurements

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

Solve both triangles


well, i drew the triangle with the measurements given and i found the rest of the sides and angles, but i dont get how to split the triangle.

 

[Denis]

What did you get for the 3rd side?

WHERE does it say that a triangle contains 2 triangles? :shock:

 

[yeunju]

So i use the law of sines to figure out the rest of angles/sides
The third side, side c = 10.6, which i put as the base of the triangle..and other angles: angle c = 50 degrees, angle b= 70 degrees..
The question doesnt say exactly where "Two triangles can be formed using the given measurements. Solve both triangles" So my problem is knowing how two can be formed...

 

[Denis]

Use law of cosines: 12^2 = 13^2 + c^2 - 2(13)(c)COS(60) ; since COS(60)=1/2, then:
c^2 - 13c + 25 = 0
Solve to get 2 solutions, hence 2 SEPARATE triangles.