Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 37.7   b = 30.5   c = 9.96

Area: T = 116.0879666039
Perimeter: p = 78.16
Semiperimeter: s = 39.08

Angle ∠ A = α = 130.1611010882° = 130°9'40″ = 2.27217381976 rad
Angle ∠ B = β = 38.19106663209° = 38°11'26″ = 0.66765528708 rad
Angle ∠ C = γ = 11.6488322797° = 11°38'54″ = 0.20333015851 rad

Height: ha = 6.15880724689
Height: hb = 7.61217813796
Height: hc = 23.30991698874

Median: ma = 12.62655019702
Median: mb = 22.97113582533
Median: mc = 33.92659428756

Inradius: r = 2.97703087523
Circumradius: R = 24.66551855375

Vertex coordinates: A[9.96; 0] B[0; 0] C[29.63106024096; 23.30991698874]
Centroid: CG[13.19768674699; 7.77697232958]
Coordinates of the circumscribed circle: U[4.98; 24.15772137798]
Coordinates of the inscribed circle: I[8.58; 2.97703087523]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 49.83989891178° = 49°50'20″ = 2.27217381976 rad
∠ B' = β' = 141.8099333679° = 141°48'34″ = 0.66765528708 rad
∠ C' = γ' = 168.3521677203° = 168°21'6″ = 0.20333015851 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 = 37.7+30.5+9.96 = 78.16 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 78.16 }{ 2 } = 39.08 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39.08 * (39.08-37.7)(39.08-30.5)(39.08-9.96) } ; ; T = sqrt{ 13474.49 } = 116.08 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 116.08 }{ 37.7 } = 6.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 116.08 }{ 30.5 } = 7.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 116.08 }{ 9.96 } = 23.31 ; ;

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{ 30.5**2+9.96**2-37.7**2 }{ 2 * 30.5 * 9.96 } ) = 130° 9'40" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 37.7**2+9.96**2-30.5**2 }{ 2 * 37.7 * 9.96 } ) = 38° 11'26" ; ;
 gamma = 180° - alpha - beta = 180° - 130° 9'40" - 38° 11'26" = 11° 38'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 116.08 }{ 39.08 } = 2.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 37.7 }{ 2 * sin 130° 9'40" } = 24.67 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 30.5**2+2 * 9.96**2 - 37.7**2 } }{ 2 } = 12.626 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.96**2+2 * 37.7**2 - 30.5**2 } }{ 2 } = 22.971 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 30.5**2+2 * 37.7**2 - 9.96**2 } }{ 2 } = 33.926 ; ;
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