Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 90   b = 100   c = 95.39

Area: T = 3897.006636098
Perimeter: p = 285.39
Semiperimeter: s = 142.695

Angle ∠ A = α = 54.79223683876° = 54°47'33″ = 0.95663072333 rad
Angle ∠ B = β = 65.21103805764° = 65°12'37″ = 1.13881358475 rad
Angle ∠ C = γ = 59.99772510361° = 59°59'50″ = 1.04771495727 rad

Height: ha = 86.66001413552
Height: hb = 77.94401272197
Height: hc = 81.70768112167

Median: ma = 86.74546024257
Median: mb = 78.11001027528
Median: mc = 82.31215239502

Inradius: r = 27.31100414239
Circumradius: R = 55.07549678391

Vertex coordinates: A[95.39; 0] B[0; 0] C[37.73658847888; 81.70768112167]
Centroid: CG[44.37552949296; 27.23656037389]
Coordinates of the circumscribed circle: U[47.695; 27.54397722845]
Coordinates of the inscribed circle: I[42.695; 27.31100414239]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.2087631612° = 125°12'27″ = 0.95663072333 rad
∠ B' = β' = 114.7989619424° = 114°47'23″ = 1.13881358475 rad
∠ C' = γ' = 120.0032748964° = 120°10″ = 1.04771495727 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 = 90+100+95.39 = 285.39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 285.39 }{ 2 } = 142.7 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 142.7 * (142.7-90)(142.7-100)(142.7-95.39) } ; ; T = sqrt{ 15186658.58 } = 3897.01 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3897.01 }{ 90 } = 86.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3897.01 }{ 100 } = 77.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3897.01 }{ 95.39 } = 81.71 ; ;

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{ 100**2+95.39**2-90**2 }{ 2 * 100 * 95.39 } ) = 54° 47'33" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 90**2+95.39**2-100**2 }{ 2 * 90 * 95.39 } ) = 65° 12'37" ; ; gamma = 180° - alpha - beta = 180° - 54° 47'33" - 65° 12'37" = 59° 59'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3897.01 }{ 142.7 } = 27.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 90 }{ 2 * sin 54° 47'33" } = 55.07 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 95.39**2 - 90**2 } }{ 2 } = 86.745 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 95.39**2+2 * 90**2 - 100**2 } }{ 2 } = 78.1 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 90**2 - 95.39**2 } }{ 2 } = 82.312 ; ;
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