Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 4.06   b = 2.5   c = 2

Area: T = 1.95548374459
Perimeter: p = 8.56
Semiperimeter: s = 4.28

Angle ∠ A = α = 128.5621916795° = 128°33'43″ = 2.24438287407 rad
Angle ∠ B = β = 28.78325690761° = 28°46'57″ = 0.50223505976 rad
Angle ∠ C = γ = 22.65655141291° = 22°39'20″ = 0.39554133153 rad

Height: ha = 0.96329741113
Height: hb = 1.56438699567
Height: hc = 1.95548374459

Median: ma = 1.0022047903
Median: mb = 2.94660651724
Median: mc = 3.22197515432

Inradius: r = 0.4576737721
Circumradius: R = 2.59661237905

Vertex coordinates: A[2; 0] B[0; 0] C[3.55884; 1.95548374459]
Centroid: CG[1.85328; 0.6521612482]
Coordinates of the circumscribed circle: U[1; 2.39658002287]
Coordinates of the inscribed circle: I[1.78; 0.4576737721]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 51.43880832052° = 51°26'17″ = 2.24438287407 rad
∠ B' = β' = 151.2177430924° = 151°13'3″ = 0.50223505976 rad
∠ C' = γ' = 157.3444485871° = 157°20'40″ = 0.39554133153 rad

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How did we calculate this triangle?

a = 4.06 ; ; b = 2.5 ; ; c = 2 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 4.06+2.5+2 = 8.56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 8.56 }{ 2 } = 4.28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.28 * (4.28-4.06)(4.28-2.5)(4.28-2) } ; ; T = sqrt{ 3.82 } = 1.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.95 }{ 4.06 } = 0.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.95 }{ 2.5 } = 1.56 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.95 }{ 2 } = 1.95 ; ;

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{ 2.5**2+2**2-4.06**2 }{ 2 * 2.5 * 2 } ) = 128° 33'43" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4.06**2+2**2-2.5**2 }{ 2 * 4.06 * 2 } ) = 28° 46'57" ; ; gamma = 180° - alpha - beta = 180° - 128° 33'43" - 28° 46'57" = 22° 39'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.95 }{ 4.28 } = 0.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4.06 }{ 2 * sin 128° 33'43" } = 2.6 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.5**2+2 * 2**2 - 4.06**2 } }{ 2 } = 1.002 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2**2+2 * 4.06**2 - 2.5**2 } }{ 2 } = 2.946 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.5**2+2 * 4.06**2 - 2**2 } }{ 2 } = 3.22 ; ;
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