+9519 Formulas for triangles?
1. Half perimeter: \(s = \dfrac{a+b+c}{2}\) where a,b,c are the side lengths of the triangle
2. Perimeter: \(P = a+b+c = 2s\) where a,b,c are the side lengths and s is the half-perimeter
3. Area formula 1: \(A=\dfrac{bh}{2}\)
where A is the area and b and h are base and height of the triangle respectively.
4. Area formula 2: \(A = \dfrac{ab\sin C}{2}\)
where A is the area and a and b are lengths of any 2 sides and C is the angle included between a and b.
5. Area formula 3: \(A = \sqrt{s(s-a)(s-b)(s-c)}\)
where A is the area nad a,b,c are side lengths and s is the half-perimeter.
6. Angle sum formula: \(\angle A + \angle B + \angle C = 180^{\circ}=\pi \text{ rad}\)
where A,B,C are the 3 interior angles of the triangle.
7. Law of Sines: \(\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)
where a,b,c are side lengths and A,B,C are the angles opposite to sides a,b,c respectively.
8. Law of Cosines: \(c^2 = a^2 + b^2 - 2ab\cos C\)
where a,b,c are side lengths and C is the angle opposite to side c.
[For special triangles]
Right angled triangle:
9. Pythagoras theorem(or Pythagorean theorem): \(a^2+b^2 = c^2\)
where c is the hypotenuse and a, b are lengths of other 2 sides.
10. No name......: \(\dfrac{1}{a^2} + \dfrac{1}{b^2} = \dfrac{1}{h^2}\)
where a and b are side lengths of the 2 legs and h is the altitude of the triangle corresponding to the hypotenuse
11. Area of right angled triangle 1: \(A = \dfrac{ab}{2}\)
where A is the area and a and b are side lengths of the 2 legs of the right triangle.
12. Area of right angled triangle 2: \(A = (s-a)(s-b) = s(s-c)\)
Where s is the half perimeter and a,b,c are side lengths.
