Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 5.78   b = 3.9   c = 1.95

Area: T = 1.22773488499
Perimeter: p = 11.63
Semiperimeter: s = 5.815

Angle ∠ A = α = 161.1699220748° = 161°10'9″ = 2.81329335549 rad
Angle ∠ B = β = 12.57991923996° = 12°34'45″ = 0.22195483246 rad
Angle ∠ C = γ = 6.25215868521° = 6°15'6″ = 0.1099110774 rad

Height: ha = 0.42546881834
Height: hb = 0.62994096666
Height: hc = 1.25988193332

Median: ma = 1.07443137344
Median: mb = 3.84774602012
Median: mc = 4.83330709699

Inradius: r = 0.21110660103
Circumradius: R = 8.95436279769

Vertex coordinates: A[1.95; 0] B[0; 0] C[5.64112564103; 1.25988193332]
Centroid: CG[2.53304188034; 0.42196064444]
Coordinates of the circumscribed circle: U[0.975; 8.99003836406]
Coordinates of the inscribed circle: I[1.915; 0.21110660103]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 18.83107792517° = 18°49'51″ = 2.81329335549 rad
∠ B' = β' = 167.42108076° = 167°25'15″ = 0.22195483246 rad
∠ C' = γ' = 173.7488413148° = 173°44'54″ = 0.1099110774 rad

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How did we calculate this triangle?

a = 5.78 ; ; b = 3.9 ; ; c = 1.95 ; ;

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

p = a+b+c = 5.78+3.9+1.95 = 11.63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.63 }{ 2 } = 5.82 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.82 * (5.82-5.78)(5.82-3.9)(5.82-1.95) } ; ; T = sqrt{ 1.51 } = 1.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.23 }{ 5.78 } = 0.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.23 }{ 3.9 } = 0.63 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.23 }{ 1.95 } = 1.26 ; ;

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{ 3.9**2+1.95**2-5.78**2 }{ 2 * 3.9 * 1.95 } ) = 161° 10'9" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.78**2+1.95**2-3.9**2 }{ 2 * 5.78 * 1.95 } ) = 12° 34'45" ; ; gamma = 180° - alpha - beta = 180° - 161° 10'9" - 12° 34'45" = 6° 15'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.23 }{ 5.82 } = 0.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.78 }{ 2 * sin 161° 10'9" } = 8.95 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.9**2+2 * 1.95**2 - 5.78**2 } }{ 2 } = 1.074 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.95**2+2 * 5.78**2 - 3.9**2 } }{ 2 } = 3.847 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.9**2+2 * 5.78**2 - 1.95**2 } }{ 2 } = 4.833 ; ;
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