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Level 473

Law of Sines & Cosines


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ambiguous case
given the measures of 2 sides and a non-included angle, there exists two possible triangles
Law of Cosines
used to solve SAS and SSS
Law of Sines
A/sin a =b/sin b= c/sin c
Sine triangle
Angle side angle
Sine triangle
Angle angle side
Angle side side
Ambiguous case, sine triangle
Area triangle
(1/2) multiplied by variables not in sin
Law of Cosines
Side angle side
Side side side
Law of cosines
Side angle side
Law of cosines
SAS
b²=a²+c²-2acCosB
A^2=(a^2-b^2-c^3)/(-2bc)
Cos a
CosB
(b^2-a^2-c^2)/(-2ac)
Sq root[s(s-a)(s-b)(s-c)]
Area using all sides
a/sinA
b/sinB=c/sinC
No triangle
Opposite< height (acute)
No triangle
Opposite</= adjacent (obtuse)
One triangle
Opposite= height (acute)
One triangle
Opposite> adjacent (acute)
One triangle
Opposite> adjacent (obtuse)
Two triangles
Height< opposite< adjacent (acute)
Height=
Adjacent(sinAngle)
A=(1/2)bcsinA
Area of an oblique triangle
a^2
b^2+c^2-2bc(cos)A
cosA
(b^2+c^2-a^2)/2bc
Heron's Area Formula
square root of