Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 100   b = 90   c = 163.29

Area: T = 3958.096567748
Perimeter: p = 353.29
Semiperimeter: s = 176.645

Angle ∠ A = α = 32.59224200732° = 32°35'33″ = 0.56988450415 rad
Angle ∠ B = β = 28.99989371321° = 28°59'56″ = 0.50661269325 rad
Angle ∠ C = γ = 118.4098642795° = 118°24'31″ = 2.06766206796 rad

Height: ha = 79.16219135497
Height: hb = 87.95876817219
Height: hc = 48.47993395491

Median: ma = 121.9911032662
Median: mb = 127.6988128608
Median: mc = 48.82771847949

Inradius: r = 22.40770631916
Circumradius: R = 92.82330467217

Vertex coordinates: A[163.29; 0] B[0; 0] C[87.46328700472; 48.47993395491]
Centroid: CG[83.58442900157; 16.16597798497]
Coordinates of the circumscribed circle: U[81.645; -44.16112044412]
Coordinates of the inscribed circle: I[86.645; 22.40770631916]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.4087579927° = 147°24'27″ = 0.56988450415 rad
∠ B' = β' = 151.0011062868° = 151°4″ = 0.50661269325 rad
∠ C' = γ' = 61.59113572053° = 61°35'29″ = 2.06766206796 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 = 100+90+163.29 = 353.29 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 353.29 }{ 2 } = 176.65 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 176.65 * (176.65-100)(176.65-90)(176.65-163.29) } ; ; T = sqrt{ 15666521.39 } = 3958.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3958.1 }{ 100 } = 79.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3958.1 }{ 90 } = 87.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3958.1 }{ 163.29 } = 48.48 ; ;

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{ 90**2+163.29**2-100**2 }{ 2 * 90 * 163.29 } ) = 32° 35'33" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 100**2+163.29**2-90**2 }{ 2 * 100 * 163.29 } ) = 28° 59'56" ; ;
 gamma = 180° - alpha - beta = 180° - 32° 35'33" - 28° 59'56" = 118° 24'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3958.1 }{ 176.65 } = 22.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 100 }{ 2 * sin 32° 35'33" } = 92.82 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 163.29**2 - 100**2 } }{ 2 } = 121.991 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 163.29**2+2 * 100**2 - 90**2 } }{ 2 } = 127.698 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 100**2 - 163.29**2 } }{ 2 } = 48.827 ; ;
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