Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 84   b = 78.81   c = 115.19

Area: T = 3310.021997207
Perimeter: p = 278
Semiperimeter: s = 139

Angle ∠ A = α = 46.82218778193° = 46°49'19″ = 0.81771959299 rad
Angle ∠ B = β = 43.17106789673° = 43°10'14″ = 0.75334704883 rad
Angle ∠ C = γ = 90.00774432134° = 90°27″ = 1.57109262354 rad

Height: ha = 78.8109999335
Height: hb = 843.9999992912
Height: hc = 57.47106132836

Median: ma = 89.3087760581
Median: mb = 92.78880058251
Median: mc = 57.58875335902

Inradius: r = 23.81330933242
Circumradius: R = 57.5955000486

Vertex coordinates: A[115.19; 0] B[0; 0] C[61.26327832277; 57.47106132836]
Centroid: CG[58.81875944092; 19.15768710945]
Coordinates of the circumscribed circle: U[57.595; -0.00774820848]
Coordinates of the inscribed circle: I[60.19; 23.81330933242]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.1788122181° = 133°10'41″ = 0.81771959299 rad
∠ B' = β' = 136.8299321033° = 136°49'46″ = 0.75334704883 rad
∠ C' = γ' = 89.99325567866° = 89°59'33″ = 1.57109262354 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 = 84+78.81+115.19 = 278 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 278 }{ 2 } = 139 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 139 * (139-84)(139-78.81)(139-115.19) } ; ; T = sqrt{ 10956232.22 } = 3310.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3310.02 }{ 84 } = 78.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3310.02 }{ 78.81 } = 84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3310.02 }{ 115.19 } = 57.47 ; ;

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{ 78.81**2+115.19**2-84**2 }{ 2 * 78.81 * 115.19 } ) = 46° 49'19" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 84**2+115.19**2-78.81**2 }{ 2 * 84 * 115.19 } ) = 43° 10'14" ; ; gamma = 180° - alpha - beta = 180° - 46° 49'19" - 43° 10'14" = 90° 27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3310.02 }{ 139 } = 23.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 84 }{ 2 * sin 46° 49'19" } = 57.6 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 78.81**2+2 * 115.19**2 - 84**2 } }{ 2 } = 89.308 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 115.19**2+2 * 84**2 - 78.81**2 } }{ 2 } = 92.788 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 78.81**2+2 * 84**2 - 115.19**2 } }{ 2 } = 57.588 ; ;
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