Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 9   b = 23   c = 23

Area: T = 101.5499692118
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 22.56656485759° = 22°33'56″ = 0.39438448655 rad
Angle ∠ B = β = 78.7177175712° = 78°43'2″ = 1.3743873894 rad
Angle ∠ C = γ = 78.7177175712° = 78°43'2″ = 1.3743873894 rad

Height: ha = 22.55554871373
Height: hb = 8.82660601842
Height: hc = 8.82660601842

Median: ma = 22.55554871373
Median: mb = 13.14334394281
Median: mc = 13.14334394281

Inradius: r = 3.69108978952
Circumradius: R = 11.72766365559

Vertex coordinates: A[23; 0] B[0; 0] C[1.76108695652; 8.82660601842]
Centroid: CG[8.25436231884; 2.94220200614]
Coordinates of the circumscribed circle: U[11.5; 2.29443419348]
Coordinates of the inscribed circle: I[4.5; 3.69108978952]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.4344351424° = 157°26'4″ = 0.39438448655 rad
∠ B' = β' = 101.2832824288° = 101°16'58″ = 1.3743873894 rad
∠ C' = γ' = 101.2832824288° = 101°16'58″ = 1.3743873894 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 = 9+23+23 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-9)(27.5-23)(27.5-23) } ; ; T = sqrt{ 10302.19 } = 101.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 101.5 }{ 9 } = 22.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 101.5 }{ 23 } = 8.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 101.5 }{ 23 } = 8.83 ; ;

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{ 23**2+23**2-9**2 }{ 2 * 23 * 23 } ) = 22° 33'56" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 9**2+23**2-23**2 }{ 2 * 9 * 23 } ) = 78° 43'2" ; ;
 gamma = 180° - alpha - beta = 180° - 22° 33'56" - 78° 43'2" = 78° 43'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 101.5 }{ 27.5 } = 3.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 9 }{ 2 * sin 22° 33'56" } = 11.73 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 23**2 - 9**2 } }{ 2 } = 22.555 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 9**2 - 23**2 } }{ 2 } = 13.143 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 9**2 - 23**2 } }{ 2 } = 13.143 ; ;
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