Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 14   b = 23   c = 23

Area: T = 153.3622316101
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 35.43878637468° = 35°26'16″ = 0.61985074023 rad
Angle ∠ B = β = 72.28110681266° = 72°16'52″ = 1.26215426257 rad
Angle ∠ C = γ = 72.28110681266° = 72°16'52″ = 1.26215426257 rad

Height: ha = 21.90989023002
Height: hb = 13.3365853574
Height: hc = 13.3365853574

Median: ma = 21.90989023002
Median: mb = 15.17439909055
Median: mc = 15.17439909055

Inradius: r = 5.11220772034
Circumradius: R = 12.07327180383

Vertex coordinates: A[23; 0] B[0; 0] C[4.26108695652; 13.3365853574]
Centroid: CG[9.08769565217; 4.44552845247]
Coordinates of the circumscribed circle: U[11.5; 3.67443054899]
Coordinates of the inscribed circle: I[7; 5.11220772034]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.5622136253° = 144°33'44″ = 0.61985074023 rad
∠ B' = β' = 107.7198931873° = 107°43'8″ = 1.26215426257 rad
∠ C' = γ' = 107.7198931873° = 107°43'8″ = 1.26215426257 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 = 14+23+23 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-14)(30-23)(30-23) } ; ; T = sqrt{ 23520 } = 153.36 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 153.36 }{ 14 } = 21.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 153.36 }{ 23 } = 13.34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 153.36 }{ 23 } = 13.34 ; ;

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**2-14**2 }{ 2 * 23 * 23 } ) = 35° 26'16" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14**2+23**2-23**2 }{ 2 * 14 * 23 } ) = 72° 16'52" ; ; gamma = 180° - alpha - beta = 180° - 35° 26'16" - 72° 16'52" = 72° 16'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 153.36 }{ 30 } = 5.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14 }{ 2 * sin 35° 26'16" } = 12.07 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 23**2 - 14**2 } }{ 2 } = 21.909 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 14**2 - 23**2 } }{ 2 } = 15.174 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 14**2 - 23**2 } }{ 2 } = 15.174 ; ;
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