Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 24.81   b = 29.59   c = 26.7

Area: T = 311.2633328344
Perimeter: p = 81.1
Semiperimeter: s = 40.55

Angle ∠ A = α = 51.99548640808° = 51°59'41″ = 0.90774815723 rad
Angle ∠ B = β = 70.01223682494° = 70°45″ = 1.22219463431 rad
Angle ∠ C = γ = 57.99327676698° = 57°59'34″ = 1.01221647382 rad

Height: ha = 25.09217636715
Height: hb = 21.03884135414
Height: hc = 23.31656051194

Median: ma = 25.30550395179
Median: mb = 21.10326307602
Median: mc = 23.81986817435

Inradius: r = 7.67660376904
Circumradius: R = 15.74332735766

Vertex coordinates: A[26.7; 0] B[0; 0] C[8.48804868914; 23.31656051194]
Centroid: CG[11.72768289638; 7.77218683731]
Coordinates of the circumscribed circle: U[13.35; 8.34443491603]
Coordinates of the inscribed circle: I[10.96; 7.67660376904]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.0055135919° = 128°19″ = 0.90774815723 rad
∠ B' = β' = 109.9887631751° = 109°59'15″ = 1.22219463431 rad
∠ C' = γ' = 122.007723233° = 122°26″ = 1.01221647382 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 = 24.81+29.59+26.7 = 81.1 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 81.1 }{ 2 } = 40.55 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 40.55 * (40.55-24.81)(40.55-29.59)(40.55-26.7) } ; ; T = sqrt{ 96884.86 } = 311.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 311.26 }{ 24.81 } = 25.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 311.26 }{ 29.59 } = 21.04 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 311.26 }{ 26.7 } = 23.32 ; ;

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{ 29.59**2+26.7**2-24.81**2 }{ 2 * 29.59 * 26.7 } ) = 51° 59'41" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 24.81**2+26.7**2-29.59**2 }{ 2 * 24.81 * 26.7 } ) = 70° 45" ; ; gamma = 180° - alpha - beta = 180° - 51° 59'41" - 70° 45" = 57° 59'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 311.26 }{ 40.55 } = 7.68 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 24.81 }{ 2 * sin 51° 59'41" } = 15.74 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 29.59**2+2 * 26.7**2 - 24.81**2 } }{ 2 } = 25.305 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 26.7**2+2 * 24.81**2 - 29.59**2 } }{ 2 } = 21.103 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 29.59**2+2 * 24.81**2 - 26.7**2 } }{ 2 } = 23.819 ; ;
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