Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 2.24   b = 4.24   c = 2.24

Area: T = 1.53334503839
Perimeter: p = 8.72
Semiperimeter: s = 4.36

Angle ∠ A = α = 18.83991969707° = 18°50'21″ = 0.32988060156 rad
Angle ∠ B = β = 142.3221606059° = 142°19'18″ = 2.48439806224 rad
Angle ∠ C = γ = 18.83991969707° = 18°50'21″ = 0.32988060156 rad

Height: ha = 1.36991521285
Height: hb = 0.72333256528
Height: hc = 1.36991521285

Median: ma = 3.22004999609
Median: mb = 0.72333256528
Median: mc = 3.22004999609

Inradius: r = 0.35217088037
Circumradius: R = 3.46884239254

Vertex coordinates: A[2.24; 0] B[0; 0] C[-1.77328571429; 1.36991521285]
Centroid: CG[0.15657142857; 0.45663840428]
Coordinates of the circumscribed circle: U[1.12; 3.28326155008]
Coordinates of the inscribed circle: I[0.12; 0.35217088037]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.1610803029° = 161°9'39″ = 0.32988060156 rad
∠ B' = β' = 37.67883939414° = 37°40'42″ = 2.48439806224 rad
∠ C' = γ' = 161.1610803029° = 161°9'39″ = 0.32988060156 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+4.24+2.24 = 8.72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 8.72 }{ 2 } = 4.36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.36 * (4.36-2.24)(4.36-4.24)(4.36-2.24) } ; ; T = sqrt{ 2.35 } = 1.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.53 }{ 2.24 } = 1.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.53 }{ 4.24 } = 0.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.53 }{ 2.24 } = 1.37 ; ;

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{ 4.24**2+2.24**2-2.24**2 }{ 2 * 4.24 * 2.24 } ) = 18° 50'21" ; ; 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**2-4.24**2 }{ 2 * 2.24 * 2.24 } ) = 142° 19'18" ; ; gamma = 180° - alpha - beta = 180° - 18° 50'21" - 142° 19'18" = 18° 50'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.53 }{ 4.36 } = 0.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.24 }{ 2 * sin 18° 50'21" } = 3.47 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.24**2+2 * 2.24**2 - 2.24**2 } }{ 2 } = 3.2 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.24**2+2 * 2.24**2 - 4.24**2 } }{ 2 } = 0.723 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.24**2+2 * 2.24**2 - 2.24**2 } }{ 2 } = 3.2 ; ;
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