Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 328.96   b = 280.51   c = 145

Area: T = 20225.55498292
Perimeter: p = 754.47
Semiperimeter: s = 377.235

Angle ∠ A = α = 966.0004607069° = 96°2″ = 1.67655241228 rad
Angle ∠ B = β = 587.9997368556° = 57°59'59″ = 1.01222863734 rad
Angle ∠ C = γ = 265.9998024375° = 25°59'59″ = 0.45437821574 rad

Height: ha = 122.9676621043
Height: hb = 144.2065552952
Height: hc = 278.9733101093

Median: ma = 151.0032515376
Median: mb = 212.0110319973
Median: mc = 296.9754781505

Inradius: r = 53.61552526389
Circumradius: R = 165.38661416

Vertex coordinates: A[145; 0] B[0; 0] C[174.3243522414; 278.9733101093]
Centroid: CG[106.4411174138; 92.99110336975]
Coordinates of the circumscribed circle: U[72.5; 148.64883294]
Coordinates of the inscribed circle: I[96.725; 53.61552526389]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 843.9995392931° = 83°59'58″ = 1.67655241228 rad
∠ B' = β' = 1222.000263144° = 122°1″ = 1.01222863734 rad
∠ C' = γ' = 1544.000197563° = 154°1″ = 0.45437821574 rad

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How did we calculate this triangle?

a = 328.96 ; ; b = 280.51 ; ; c = 145 ; ;

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

p = a+b+c = 328.96+280.51+145 = 754.47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 754.47 }{ 2 } = 377.24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 377.24 * (377.24-328.96)(377.24-280.51)(377.24-145) } ; ; T = sqrt{ 409072865.89 } = 20225.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 20225.55 }{ 328.96 } = 122.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 20225.55 }{ 280.51 } = 144.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 20225.55 }{ 145 } = 278.97 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 280.51**2+145**2-328.96**2 }{ 2 * 280.51 * 145 } ) = 96° 2" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 328.96**2+145**2-280.51**2 }{ 2 * 328.96 * 145 } ) = 57° 59'59" ; ; gamma = 180° - alpha - beta = 180° - 96° 2" - 57° 59'59" = 25° 59'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 20225.55 }{ 377.24 } = 53.62 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 328.96 }{ 2 * sin 96° 2" } = 165.39 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 280.51**2+2 * 145**2 - 328.96**2 } }{ 2 } = 151.003 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 145**2+2 * 328.96**2 - 280.51**2 } }{ 2 } = 212.01 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 280.51**2+2 * 328.96**2 - 145**2 } }{ 2 } = 296.975 ; ;
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