Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 75.9   b = 80   c = 56

Area: T = 2031.464407278
Perimeter: p = 211.9
Semiperimeter: s = 105.95

Angle ∠ A = α = 65.08108994062° = 65°4'51″ = 1.13658759748 rad
Angle ∠ B = β = 72.92195182918° = 72°55'10″ = 1.27326856832 rad
Angle ∠ C = γ = 421.999582302° = 41°59'58″ = 0.73330309956 rad

Height: ha = 53.5330015093
Height: hb = 50.78766018195
Height: hc = 72.55222883136

Median: ma = 57.68770652746
Median: mb = 53.37704506258
Median: mc = 72.77664041431

Inradius: r = 19.17437996487
Circumradius: R = 41.84656822048

Vertex coordinates: A[56; 0] B[0; 0] C[22.29329464286; 72.55222883136]
Centroid: CG[26.09876488095; 24.18440961045]
Coordinates of the circumscribed circle: U[28; 31.09876063257]
Coordinates of the inscribed circle: I[25.95; 19.17437996487]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.9199100594° = 114°55'9″ = 1.13658759748 rad
∠ B' = β' = 107.0880481708° = 107°4'50″ = 1.27326856832 rad
∠ C' = γ' = 1388.000417698° = 138°2″ = 0.73330309956 rad

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How did we calculate this triangle?

a = 75.9 ; ; b = 80 ; ; c = 56 ; ;

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

p = a+b+c = 75.9+80+56 = 211.9 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 211.9 }{ 2 } = 105.95 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 105.95 * (105.95-75.9)(105.95-80)(105.95-56) } ; ; T = sqrt{ 4126846.28 } = 2031.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2031.46 }{ 75.9 } = 53.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2031.46 }{ 80 } = 50.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2031.46 }{ 56 } = 72.55 ; ;

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{ 80**2+56**2-75.9**2 }{ 2 * 80 * 56 } ) = 65° 4'51" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 75.9**2+56**2-80**2 }{ 2 * 75.9 * 56 } ) = 72° 55'10" ; ; gamma = 180° - alpha - beta = 180° - 65° 4'51" - 72° 55'10" = 41° 59'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2031.46 }{ 105.95 } = 19.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 75.9 }{ 2 * sin 65° 4'51" } = 41.85 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 80**2+2 * 56**2 - 75.9**2 } }{ 2 } = 57.687 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 56**2+2 * 75.9**2 - 80**2 } }{ 2 } = 53.37 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 80**2+2 * 75.9**2 - 56**2 } }{ 2 } = 72.776 ; ;
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