Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 2.24   b = 3.16   c = 2.24

Area: T = 2.50987693557
Perimeter: p = 7.64
Semiperimeter: s = 3.82

Angle ∠ A = α = 45.14215956949° = 45°8'30″ = 0.78878694745 rad
Angle ∠ B = β = 89.71768086102° = 89°43'1″ = 1.56658537046 rad
Angle ∠ C = γ = 45.14215956949° = 45°8'30″ = 0.78878694745 rad

Height: ha = 2.2439972639
Height: hb = 1.58878287061
Height: hc = 2.2439972639

Median: ma = 2.49994399373
Median: mb = 1.58878287061
Median: mc = 2.49994399373

Inradius: r = 0.65767459046
Circumradius: R = 1.58800192995

Vertex coordinates: A[2.24; 0] B[0; 0] C[0.01110714286; 2.2439972639]
Centroid: CG[0.75503571429; 0.74766575463]
Coordinates of the circumscribed circle: U[1.12; 1.11444778988]
Coordinates of the inscribed circle: I[0.66; 0.65767459046]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.8588404305° = 134°51'30″ = 0.78878694745 rad
∠ B' = β' = 90.28331913898° = 90°16'59″ = 1.56658537046 rad
∠ C' = γ' = 134.8588404305° = 134°51'30″ = 0.78878694745 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 = 2.24+3.16+2.24 = 7.64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 7.64 }{ 2 } = 3.82 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.82 * (3.82-2.24)(3.82-3.16)(3.82-2.24) } ; ; T = sqrt{ 6.29 } = 2.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.51 }{ 2.24 } = 2.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.51 }{ 3.16 } = 1.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.51 }{ 2.24 } = 2.24 ; ;

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{ 3.16**2+2.24**2-2.24**2 }{ 2 * 3.16 * 2.24 } ) = 45° 8'30" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.24**2+2.24**2-3.16**2 }{ 2 * 2.24 * 2.24 } ) = 89° 43'1" ; ; gamma = 180° - alpha - beta = 180° - 45° 8'30" - 89° 43'1" = 45° 8'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.51 }{ 3.82 } = 0.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.24 }{ 2 * sin 45° 8'30" } = 1.58 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.16**2+2 * 2.24**2 - 2.24**2 } }{ 2 } = 2.499 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.24**2+2 * 2.24**2 - 3.16**2 } }{ 2 } = 1.588 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.16**2+2 * 2.24**2 - 2.24**2 } }{ 2 } = 2.499 ; ;
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