Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 26.7   b = 31.2   c = 27.03

Area: T = 341.1788351689
Perimeter: p = 84.93
Semiperimeter: s = 42.465

Angle ∠ A = α = 54.01096579884° = 54°35″ = 0.94326463598 rad
Angle ∠ B = β = 70.99439051332° = 70°59'38″ = 1.23990773934 rad
Angle ∠ C = γ = 54.99664368784° = 54°59'47″ = 0.96598689004 rad

Height: ha = 25.55664308381
Height: hb = 21.87704071595
Height: hc = 25.24444211386

Median: ma = 25.95878109632
Median: mb = 21.87222529704
Median: mc = 25.77003847247

Inradius: r = 8.03443424394
Circumradius: R = 16.49994870634

Vertex coordinates: A[27.03; 0] B[0; 0] C[8.69553551609; 25.24444211386]
Centroid: CG[11.90884517203; 8.41548070462]
Coordinates of the circumscribed circle: U[13.515; 9.46545574833]
Coordinates of the inscribed circle: I[11.265; 8.03443424394]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.9990342012° = 125°59'25″ = 0.94326463598 rad
∠ B' = β' = 109.0066094867° = 109°22″ = 1.23990773934 rad
∠ C' = γ' = 125.0043563122° = 125°13″ = 0.96598689004 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 = 26.7+31.2+27.03 = 84.93 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 84.93 }{ 2 } = 42.47 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 42.47 * (42.47-26.7)(42.47-31.2)(42.47-27.03) } ; ; T = sqrt{ 116402.67 } = 341.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 341.18 }{ 26.7 } = 25.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 341.18 }{ 31.2 } = 21.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 341.18 }{ 27.03 } = 25.24 ; ;

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{ 31.2**2+27.03**2-26.7**2 }{ 2 * 31.2 * 27.03 } ) = 54° 35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 26.7**2+27.03**2-31.2**2 }{ 2 * 26.7 * 27.03 } ) = 70° 59'38" ; ;
 gamma = 180° - alpha - beta = 180° - 54° 35" - 70° 59'38" = 54° 59'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 341.18 }{ 42.47 } = 8.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 26.7 }{ 2 * sin 54° 35" } = 16.5 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 31.2**2+2 * 27.03**2 - 26.7**2 } }{ 2 } = 25.958 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 27.03**2+2 * 26.7**2 - 31.2**2 } }{ 2 } = 21.872 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 31.2**2+2 * 26.7**2 - 27.03**2 } }{ 2 } = 25.7 ; ;
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