Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 0.03   b = 0.05   c = 0.06

Area: T = 0.00107483315
Perimeter: p = 0.14
Semiperimeter: s = 0.07

Angle ∠ A = α = 29.92664348666° = 29°55'35″ = 0.52223148218 rad
Angle ∠ B = β = 56.25110114041° = 56°15'4″ = 0.98217653566 rad
Angle ∠ C = γ = 93.82325537293° = 93°49'21″ = 1.63875124752 rad

Height: ha = 0.05498887652
Height: hb = 0.03299332591
Height: hc = 0.02549443826

Median: ma = 0.05331507291
Median: mb = 0.04403112887
Median: mc = 0.02882842712

Inradius: r = 0.01106904497
Circumradius: R = 0.03300668897

Vertex coordinates: A[0.06; 0] B[0; 0] C[0.01766666667; 0.02549443826]
Centroid: CG[0.02655555556; 0.00883147942]
Coordinates of the circumscribed circle: U[0.03; -0.00220044593]
Coordinates of the inscribed circle: I[0.02; 0.01106904497]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0743565133° = 150°4'25″ = 0.52223148218 rad
∠ B' = β' = 123.7498988596° = 123°44'56″ = 0.98217653566 rad
∠ C' = γ' = 86.17774462707° = 86°10'39″ = 1.63875124752 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 = 0.03+0.05+0.06 = 0.14 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 0.14 }{ 2 } = 0.07 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.07 * (0.07-0.03)(0.07-0.05)(0.07-0.06) } ; ; T = sqrt{ 0 } = 0 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0 }{ 0.03 } = 0.05 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0 }{ 0.05 } = 0.03 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0 }{ 0.06 } = 0.02 ; ;

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{ 0.05**2+0.06**2-0.03**2 }{ 2 * 0.05 * 0.06 } ) = 29° 55'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 0.03**2+0.06**2-0.05**2 }{ 2 * 0.03 * 0.06 } ) = 56° 15'4" ; ; gamma = 180° - alpha - beta = 180° - 29° 55'35" - 56° 15'4" = 93° 49'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0 }{ 0.07 } = 0.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 0.03 }{ 2 * sin 29° 55'35" } = 0.03 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.05**2+2 * 0.06**2 - 0.03**2 } }{ 2 } = 0.053 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.06**2+2 * 0.03**2 - 0.05**2 } }{ 2 } = 0.04 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.05**2+2 * 0.03**2 - 0.06**2 } }{ 2 } = 0.028 ; ;
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