Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 15.79   b = 13.4   c = 28.79

Area: T = 34.54221311444
Perimeter: p = 57.98
Semiperimeter: s = 28.99

Angle ∠ A = α = 10.31658306167° = 10°18'57″ = 0.18800452093 rad
Angle ∠ B = β = 8.74110568358° = 8°44'28″ = 0.15325602219 rad
Angle ∠ C = γ = 160.9433112548° = 160°56'35″ = 2.80989872224 rad

Height: ha = 4.37551907719
Height: hb = 5.15655419619
Height: hc = 2.4399592299

Median: ma = 21.02109663194
Median: mb = 22.23107017433
Median: mc = 2.68881266711

Inradius: r = 1.19215188391
Circumradius: R = 44.08879061177

Vertex coordinates: A[28.79; 0] B[0; 0] C[15.60766029871; 2.4399592299]
Centroid: CG[14.79988676624; 0.87998640997]
Coordinates of the circumscribed circle: U[14.395; -41.67216623239]
Coordinates of the inscribed circle: I[15.59; 1.19215188391]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.6844169383° = 169°41'3″ = 0.18800452093 rad
∠ B' = β' = 171.2598943164° = 171°15'32″ = 0.15325602219 rad
∠ C' = γ' = 19.05768874525° = 19°3'25″ = 2.80989872224 rad

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How did we calculate this triangle?

a = 15.79 ; ; b = 13.4 ; ; c = 28.79 ; ;

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

p = a+b+c = 15.79+13.4+28.79 = 57.98 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57.98 }{ 2 } = 28.99 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.99 * (28.99-15.79)(28.99-13.4)(28.99-28.79) } ; ; T = sqrt{ 1193.16 } = 34.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34.54 }{ 15.79 } = 4.38 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34.54 }{ 13.4 } = 5.16 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34.54 }{ 28.79 } = 2.4 ; ;

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{ 13.4**2+28.79**2-15.79**2 }{ 2 * 13.4 * 28.79 } ) = 10° 18'57" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 15.79**2+28.79**2-13.4**2 }{ 2 * 15.79 * 28.79 } ) = 8° 44'28" ; ; gamma = 180° - alpha - beta = 180° - 10° 18'57" - 8° 44'28" = 160° 56'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34.54 }{ 28.99 } = 1.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 15.79 }{ 2 * sin 10° 18'57" } = 44.09 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.4**2+2 * 28.79**2 - 15.79**2 } }{ 2 } = 21.021 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28.79**2+2 * 15.79**2 - 13.4**2 } }{ 2 } = 22.231 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.4**2+2 * 15.79**2 - 28.79**2 } }{ 2 } = 2.688 ; ;
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