Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 12.35   b = 8.75   c = 5.25

Area: T = 19.52435396681
Perimeter: p = 26.35
Semiperimeter: s = 13.175

Angle ∠ A = α = 121.788784681° = 121°47'16″ = 2.12655989158 rad
Angle ∠ B = β = 37.03297679628° = 37°1'47″ = 0.64662913722 rad
Angle ∠ C = γ = 21.1822385227° = 21°10'57″ = 0.37697023656 rad

Height: ha = 3.16217068288
Height: hb = 4.46325233527
Height: hc = 7.43875389212

Median: ma = 3.7332542699
Median: mb = 8.42203251125
Median: mc = 10.37655421545

Inradius: r = 1.48218625934
Circumradius: R = 7.26546678656

Vertex coordinates: A[5.25; 0] B[0; 0] C[9.85992857143; 7.43875389212]
Centroid: CG[5.03664285714; 2.47991796404]
Coordinates of the circumscribed circle: U[2.625; 6.77438300981]
Coordinates of the inscribed circle: I[4.425; 1.48218625934]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 58.21221531898° = 58°12'44″ = 2.12655989158 rad
∠ B' = β' = 142.9770232037° = 142°58'13″ = 0.64662913722 rad
∠ C' = γ' = 158.8187614773° = 158°49'3″ = 0.37697023656 rad

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How did we calculate this triangle?

a = 12.35 ; ; b = 8.75 ; ; c = 5.25 ; ;

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

p = a+b+c = 12.35+8.75+5.25 = 26.35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 26.35 }{ 2 } = 13.18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.18 * (13.18-12.35)(13.18-8.75)(13.18-5.25) } ; ; T = sqrt{ 381.17 } = 19.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19.52 }{ 12.35 } = 3.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19.52 }{ 8.75 } = 4.46 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19.52 }{ 5.25 } = 7.44 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 12.35**2-8.75**2-5.25**2 }{ 2 * 8.75 * 5.25 } ) = 121° 47'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8.75**2-12.35**2-5.25**2 }{ 2 * 12.35 * 5.25 } ) = 37° 1'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.25**2-12.35**2-8.75**2 }{ 2 * 8.75 * 12.35 } ) = 21° 10'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19.52 }{ 13.18 } = 1.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12.35 }{ 2 * sin 121° 47'16" } = 7.26 ; ;

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