Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 3   b = 26   c = 28

Area: T = 30.14402969461
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 4.75497013846° = 4°44'59″ = 0.08328979276 rad
Angle ∠ B = β = 45.85988345181° = 45°51'32″ = 0.88003876535 rad
Angle ∠ C = γ = 129.3911464097° = 129°23'29″ = 2.25883070725 rad

Height: ha = 20.09435312974
Height: hb = 2.31884843805
Height: hc = 2.15328783533

Median: ma = 26.97768419204
Median: mb = 15.0833103129
Median: mc = 12.10437184369

Inradius: r = 1.05875542788
Circumradius: R = 18.11552827053

Vertex coordinates: A[28; 0] B[0; 0] C[2.08992857143; 2.15328783533]
Centroid: CG[10.03297619048; 0.71876261178]
Coordinates of the circumscribed circle: U[14; -11.49662371014]
Coordinates of the inscribed circle: I[2.5; 1.05875542788]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.2550298615° = 175°15'1″ = 0.08328979276 rad
∠ B' = β' = 134.1411165482° = 134°8'28″ = 0.88003876535 rad
∠ C' = γ' = 50.60985359027° = 50°36'31″ = 2.25883070725 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 = 3+26+28 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-3)(28.5-26)(28.5-28) } ; ; T = sqrt{ 908.44 } = 30.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 30.14 }{ 3 } = 20.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 30.14 }{ 26 } = 2.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 30.14 }{ 28 } = 2.15 ; ;

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{ 26**2+28**2-3**2 }{ 2 * 26 * 28 } ) = 4° 44'59" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3**2+28**2-26**2 }{ 2 * 3 * 28 } ) = 45° 51'32" ; ;
 gamma = 180° - alpha - beta = 180° - 4° 44'59" - 45° 51'32" = 129° 23'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 30.14 }{ 28.5 } = 1.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3 }{ 2 * sin 4° 44'59" } = 18.12 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 28**2 - 3**2 } }{ 2 } = 26.977 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 3**2 - 26**2 } }{ 2 } = 15.083 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 3**2 - 28**2 } }{ 2 } = 12.104 ; ;
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