Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 38   b = 34   c = 48.76

Area: T = 643.6021511058
Perimeter: p = 120.76
Semiperimeter: s = 60.38

Angle ∠ A = α = 50.93552078843° = 50°56'7″ = 0.88989870828 rad
Angle ∠ B = β = 44.00436291363° = 44°13″ = 0.76880082113 rad
Angle ∠ C = γ = 85.06111629794° = 85°3'40″ = 1.48545973596 rad

Height: ha = 33.87437637399
Height: hb = 37.85989124152
Height: hc = 26.39987494282

Median: ma = 37.4943583451
Median: mb = 40.27111906951
Median: mc = 26.56334259839

Inradius: r = 10.65991836876
Circumradius: R = 24.47108561577

Vertex coordinates: A[48.76; 0] B[0; 0] C[27.3333240361; 26.39987494282]
Centroid: CG[25.36444134537; 8.87995831427]
Coordinates of the circumscribed circle: U[24.38; 2.10767513123]
Coordinates of the inscribed circle: I[26.38; 10.65991836876]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.0654792116° = 129°3'53″ = 0.88989870828 rad
∠ B' = β' = 135.9966370864° = 135°59'47″ = 0.76880082113 rad
∠ C' = γ' = 94.93988370206° = 94°56'20″ = 1.48545973596 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 = 38+34+48.76 = 120.76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 120.76 }{ 2 } = 60.38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 60.38 * (60.38-38)(60.38-34)(60.38-48.76) } ; ; T = sqrt{ 414222.91 } = 643.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 643.6 }{ 38 } = 33.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 643.6 }{ 34 } = 37.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 643.6 }{ 48.76 } = 26.4 ; ;

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{ 34**2+48.76**2-38**2 }{ 2 * 34 * 48.76 } ) = 50° 56'7" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 38**2+48.76**2-34**2 }{ 2 * 38 * 48.76 } ) = 44° 13" ; ; gamma = 180° - alpha - beta = 180° - 50° 56'7" - 44° 13" = 85° 3'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 643.6 }{ 60.38 } = 10.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 38 }{ 2 * sin 50° 56'7" } = 24.47 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 34**2+2 * 48.76**2 - 38**2 } }{ 2 } = 37.494 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 48.76**2+2 * 38**2 - 34**2 } }{ 2 } = 40.271 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 34**2+2 * 38**2 - 48.76**2 } }{ 2 } = 26.563 ; ;
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