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Law of Sines

sinA/a = sinB/b = sinC/c

Law of Sines (info needed)

-2 side lengths and 1 angle measure

-2 angle measures and 1 side length

-2 angle measures and 1 side length

Area of Any Triangle

(1/2)(a)(b)(sinC)

Law of Cosines

c²=a²+b²-2ab(cosC)

Law of Cosines (info needed)

2 side lengths, included angle and measure of angle that corresponds with the length you're trying to find

Ambiguous Case: Acute Angles

No Triangles: a < height

1 Triangle: a ≥ b, a = height

2 Triangles: height < a < b

1 Triangle: a ≥ b, a = height

2 Triangles: height < a < b

Ambiguous Case: Obtuse Angles

None: a ≤ height

1 Triangle: a > b

**2 triangles cannot be formed because of the angle placement, it can't be moved

1 Triangle: a > b

**2 triangles cannot be formed because of the angle placement, it can't be moved