Angle Classification
Perimeter- Area Formulas
- Volume Formulas
- Triangles
- Parallelogram
- Circle
- Central Median
- Pythagorean Theorem Problems
- Sine Cosine Rule
- Trigonometry
- Definition of line slope
- Vectors
- Analytic Geometry
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Sine Rule
In a triangle ABC the area is:
S = a.c.sin(B)/2 = b.c.sin(A)/2 = a.b.sin(C)/2
=>
a.c.sin(B) = b.c.sin(A) = a.b.sin(C)
dividing through by a.b.c, we get the sine formula
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Say R is the radius of the circle with center O through the points A,B and C(for every 3 points that do not lie in a line there is 1 circle that the points belong to) of triangle ABC.
Let B' be the second intersection point of BO and the circle. The
angle B' in triangle BB'C is equal to A, and the triangle BB'C is a right triangle
=> a = 2Rsin(B') = 2Rsin(A) then we have:
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= | 2R |
Cosine(Cos) Rule
a2 = b2 + c2 - 2 b c cos(A)
b2 = c2 + a2 - 2 c a cos(B)
c2 = a2 + b2 - 2 a b cos(C)
b2 = c2 + a2 - 2 c a cos(B)
c2 = a2 + b2 - 2 a b cos(C)
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