Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 37.7   b = 30.5   c = 49.29

Area: T = 574.5954514044
Perimeter: p = 117.49
Semiperimeter: s = 58.745

Angle ∠ A = α = 49.85655409964° = 49°51'20″ = 0.87701433408 rad
Angle ∠ B = β = 38.2021653416° = 38°12'6″ = 0.66767446318 rad
Angle ∠ C = γ = 91.94328055875° = 91°56'34″ = 1.6054704681 rad

Height: ha = 30.48224675885
Height: hb = 37.67883287898
Height: hc = 23.31548514524

Median: ma = 36.39444302057
Median: mb = 41.14440706542
Median: mc = 23.84110145548

Inradius: r = 9.78111645935
Circumradius: R = 24.65991749115

Vertex coordinates: A[49.29; 0] B[0; 0] C[29.62661320755; 23.31548514524]
Centroid: CG[26.30553773585; 7.77216171508]
Coordinates of the circumscribed circle: U[24.645; -0.83659918158]
Coordinates of the inscribed circle: I[28.245; 9.78111645935]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.1444459004° = 130°8'40″ = 0.87701433408 rad
∠ B' = β' = 141.7988346584° = 141°47'54″ = 0.66767446318 rad
∠ C' = γ' = 88.05771944125° = 88°3'26″ = 1.6054704681 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+49.29 = 117.49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 117.49 }{ 2 } = 58.75 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 58.75 * (58.75-37.7)(58.75-30.5)(58.75-49.29) } ; ; T = sqrt{ 330158.86 } = 574.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 574.59 }{ 37.7 } = 30.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 574.59 }{ 30.5 } = 37.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 574.59 }{ 49.29 } = 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+49.29**2-37.7**2 }{ 2 * 30.5 * 49.29 } ) = 49° 51'20" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 37.7**2+49.29**2-30.5**2 }{ 2 * 37.7 * 49.29 } ) = 38° 12'6" ; ; gamma = 180° - alpha - beta = 180° - 49° 51'20" - 38° 12'6" = 91° 56'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 574.59 }{ 58.75 } = 9.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 37.7 }{ 2 * sin 49° 51'20" } = 24.66 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 30.5**2+2 * 49.29**2 - 37.7**2 } }{ 2 } = 36.394 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 49.29**2+2 * 37.7**2 - 30.5**2 } }{ 2 } = 41.144 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 30.5**2+2 * 37.7**2 - 49.29**2 } }{ 2 } = 23.841 ; ;
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