Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 59   b = 40   c = 57.91

Area: T = 1098.134418553
Perimeter: p = 156.91
Semiperimeter: s = 78.455

Angle ∠ A = α = 71.46766227896° = 71°28' = 1.2477327873 rad
Angle ∠ B = β = 40.00113654113° = 40°5″ = 0.69881555317 rad
Angle ∠ C = γ = 68.53220117991° = 68°31'55″ = 1.19661092489 rad

Height: ha = 37.22548876451
Height: hb = 54.90767092765
Height: hc = 37.9265546038

Median: ma = 40.08215924085
Median: mb = 54.93298102127
Median: mc = 41.25766112884

Inradius: r = 13.9976994271
Circumradius: R = 31.11435929017

Vertex coordinates: A[57.91; 0] B[0; 0] C[45.19657183561; 37.9265546038]
Centroid: CG[34.36985727854; 12.64218486793]
Coordinates of the circumscribed circle: U[28.955; 11.38769942589]
Coordinates of the inscribed circle: I[38.455; 13.9976994271]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 108.533337721° = 108°32' = 1.2477327873 rad
∠ B' = β' = 139.9998634589° = 139°59'55″ = 0.69881555317 rad
∠ C' = γ' = 111.4687988201° = 111°28'5″ = 1.19661092489 rad

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How did we calculate this triangle?

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

p = a+b+c = 59+40+57.91 = 156.91 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 156.91 }{ 2 } = 78.46 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 78.46 * (78.46-59)(78.46-40)(78.46-57.91) } ; ; T = sqrt{ 1205898.69 } = 1098.13 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1098.13 }{ 59 } = 37.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1098.13 }{ 40 } = 54.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1098.13 }{ 57.91 } = 37.93 ; ;

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{ 40**2+57.91**2-59**2 }{ 2 * 40 * 57.91 } ) = 71° 28' ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 59**2+57.91**2-40**2 }{ 2 * 59 * 57.91 } ) = 40° 5" ; ; gamma = 180° - alpha - beta = 180° - 71° 28' - 40° 5" = 68° 31'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1098.13 }{ 78.46 } = 14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 59 }{ 2 * sin 71° 28' } = 31.11 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 40**2+2 * 57.91**2 - 59**2 } }{ 2 } = 40.082 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 57.91**2+2 * 59**2 - 40**2 } }{ 2 } = 54.93 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 40**2+2 * 59**2 - 57.91**2 } }{ 2 } = 41.257 ; ;
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