Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 522.03   b = 3623.57   c = 4000

Area: T = 687714.0220133
Perimeter: p = 8145.6
Semiperimeter: s = 4072.8

Angle ∠ A = α = 5.44552500058° = 5°26'43″ = 0.09550375412 rad
Angle ∠ B = β = 41.22001971017° = 41°12'1″ = 0.71990790919 rad
Angle ∠ C = γ = 133.3554552893° = 133°21'16″ = 2.32774760205 rad

Height: ha = 2634.768819391
Height: hb = 379.5788161941
Height: hc = 343.8577010066

Median: ma = 3807.493273699
Median: mb = 2203.110979623
Median: mc = 1643.598980068

Inradius: r = 168.8555337884
Circumradius: R = 2750.587973478

Vertex coordinates: A[4000; 0] B[0; 0] C[392.7821972; 343.8577010066]
Centroid: CG[1464.261065733; 114.6199003355]
Coordinates of the circumscribed circle: U[2000; -1888.303317411]
Coordinates of the inscribed circle: I[449.23; 168.8555337884]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.5554749994° = 174°33'17″ = 0.09550375412 rad
∠ B' = β' = 138.8799802898° = 138°47'59″ = 0.71990790919 rad
∠ C' = γ' = 46.64554471074° = 46°38'44″ = 2.32774760205 rad

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How did we calculate this triangle?

a = 522.03 ; ; b = 3623.57 ; ; c = 4000 ; ;

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

p = a+b+c = 522.03+3623.57+4000 = 8145.6 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 8145.6 }{ 2 } = 4072.8 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4072.8 * (4072.8-522.03)(4072.8-3623.57)(4072.8-4000) } ; ; T = sqrt{ 472950573487 } = 687714.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 687714.02 }{ 522.03 } = 2634.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 687714.02 }{ 3623.57 } = 379.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 687714.02 }{ 4000 } = 343.86 ; ;

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{ 522.03**2-3623.57**2-4000**2 }{ 2 * 3623.57 * 4000 } ) = 5° 26'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 3623.57**2-522.03**2-4000**2 }{ 2 * 522.03 * 4000 } ) = 41° 12'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4000**2-522.03**2-3623.57**2 }{ 2 * 3623.57 * 522.03 } ) = 133° 21'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 687714.02 }{ 4072.8 } = 168.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 522.03 }{ 2 * sin 5° 26'43" } = 2750.58 ; ;




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