Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 2.88   b = 1.1   c = 2.66

Area: T = 1.46329983459
Perimeter: p = 6.64
Semiperimeter: s = 3.32

Angle ∠ A = α = 90.08661590994° = 90°5'10″ = 1.57223000868 rad
Angle ∠ B = β = 22.45441513641° = 22°27'15″ = 0.3921898872 rad
Angle ∠ C = γ = 67.46596895365° = 67°27'35″ = 1.17773936948 rad

Height: ha = 1.01659710735
Height: hb = 2.66599969925
Height: hc = 1.10999987563

Median: ma = 1.43884714109
Median: mb = 2.71770756338
Median: mc = 1.7277223205

Inradius: r = 0.44106621524
Circumradius: R = 1.44400016281

Vertex coordinates: A[2.66; 0] B[0; 0] C[2.66216541353; 1.10999987563]
Centroid: CG[1.77438847118; 0.36766662521]
Coordinates of the circumscribed circle: U[1.33; 0.55220006241]
Coordinates of the inscribed circle: I[2.22; 0.44106621524]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 89.91438409006° = 89°54'50″ = 1.57223000868 rad
∠ B' = β' = 157.5465848636° = 157°32'45″ = 0.3921898872 rad
∠ C' = γ' = 112.5440310464° = 112°32'25″ = 1.17773936948 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 = 2.88+1.1+2.66 = 6.64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 6.64 }{ 2 } = 3.32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.32 * (3.32-2.88)(3.32-1.1)(3.32-2.66) } ; ; T = sqrt{ 2.14 } = 1.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.46 }{ 2.88 } = 1.02 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.46 }{ 1.1 } = 2.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.46 }{ 2.66 } = 1.1 ; ;

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{ 1.1**2+2.66**2-2.88**2 }{ 2 * 1.1 * 2.66 } ) = 90° 5'10" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.88**2+2.66**2-1.1**2 }{ 2 * 2.88 * 2.66 } ) = 22° 27'15" ; ; gamma = 180° - alpha - beta = 180° - 90° 5'10" - 22° 27'15" = 67° 27'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.46 }{ 3.32 } = 0.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.88 }{ 2 * sin 90° 5'10" } = 1.44 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.1**2+2 * 2.66**2 - 2.88**2 } }{ 2 } = 1.438 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.66**2+2 * 2.88**2 - 1.1**2 } }{ 2 } = 2.717 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.1**2+2 * 2.88**2 - 2.66**2 } }{ 2 } = 1.727 ; ;
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