12 20 26 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 20   c = 26

Area: T = 115.3733307138
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 26.34329755443° = 26°20'35″ = 0.4659771658 rad
Angle ∠ B = β = 47.69550102928° = 47°41'42″ = 0.83224349664 rad
Angle ∠ C = γ = 105.9622014163° = 105°57'43″ = 1.84993860292 rad

Height: ha = 19.2298884523
Height: hb = 11.53773307138
Height: hc = 8.87548697799

Median: ma = 22.40553565024
Median: mb = 17.60768168617
Median: mc = 10.14988915651

Inradius: r = 3.97883899013
Circumradius: R = 13.52113251548

Vertex coordinates: A[26; 0] B[0; 0] C[8.07769230769; 8.87548697799]
Centroid: CG[11.3598974359; 2.95882899266]
Coordinates of the circumscribed circle: U[13; -3.71883644176]
Coordinates of the inscribed circle: I[9; 3.97883899013]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.6577024456° = 153°39'25″ = 0.4659771658 rad
∠ B' = β' = 132.3054989707° = 132°18'18″ = 0.83224349664 rad
∠ C' = γ' = 74.03879858372° = 74°2'17″ = 1.84993860292 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 12 ; ; b = 20 ; ; c = 26 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 12+20+26 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-12)(29-20)(29-26) } ; ; T = sqrt{ 13311 } = 115.37 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 115.37 }{ 12 } = 19.23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 115.37 }{ 20 } = 11.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 115.37 }{ 26 } = 8.87 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 12**2-20**2-26**2 }{ 2 * 20 * 26 } ) = 26° 20'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-12**2-26**2 }{ 2 * 12 * 26 } ) = 47° 41'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-12**2-20**2 }{ 2 * 20 * 12 } ) = 105° 57'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 115.37 }{ 29 } = 3.98 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 26° 20'35" } = 13.52 ; ;




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