Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 0.81   b = 0.47   c = 0.94

Area: T = 0.19903428486
Perimeter: p = 2.22
Semiperimeter: s = 1.11

Angle ∠ A = α = 59.50545828523° = 59°30'16″ = 1.03985508908 rad
Angle ∠ B = β = 29.99987572048° = 29°59'56″ = 0.52435770847 rad
Angle ∠ C = γ = 90.4976659943° = 90°29'48″ = 1.57994646781 rad

Height: ha = 0.47699823421
Height: hb = 0.81099695684
Height: hc = 0.40549847842

Median: ma = 0.62330770418
Median: mb = 0.8455354955
Median: mc = 0.46664761516

Inradius: r = 0.17114800438
Circumradius: R = 0.47700176585

Vertex coordinates: A[0.94; 0] B[0; 0] C[0.70114893617; 0.40549847842]
Centroid: CG[0.54771631206; 0.13549949281]
Coordinates of the circumscribed circle: U[0.47; -0.00440742271]
Coordinates of the inscribed circle: I[0.64; 0.17114800438]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120.4955417148° = 120°29'44″ = 1.03985508908 rad
∠ B' = β' = 150.0011242795° = 150°4″ = 0.52435770847 rad
∠ C' = γ' = 89.5033340057° = 89°30'12″ = 1.57994646781 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 = 0.81+0.47+0.94 = 2.22 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2.22 }{ 2 } = 1.11 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1.11 * (1.11-0.81)(1.11-0.47)(1.11-0.94) } ; ; T = sqrt{ 0.04 } = 0.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.19 }{ 0.81 } = 0.47 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.19 }{ 0.47 } = 0.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.19 }{ 0.94 } = 0.4 ; ;

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{ 0.47**2+0.94**2-0.81**2 }{ 2 * 0.47 * 0.94 } ) = 59° 30'16" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 0.81**2+0.94**2-0.47**2 }{ 2 * 0.81 * 0.94 } ) = 29° 59'56" ; ; gamma = 180° - alpha - beta = 180° - 59° 30'16" - 29° 59'56" = 90° 29'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.19 }{ 1.11 } = 0.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 0.81 }{ 2 * sin 59° 30'16" } = 0.47 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.47**2+2 * 0.94**2 - 0.81**2 } }{ 2 } = 0.623 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.94**2+2 * 0.81**2 - 0.47**2 } }{ 2 } = 0.845 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.47**2+2 * 0.81**2 - 0.94**2 } }{ 2 } = 0.466 ; ;
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