Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 5.2   b = 5.2   c = 10.28

Area: T = 4.0498545398
Perimeter: p = 20.68
Semiperimeter: s = 10.34

Angle ∠ A = α = 8.71222446146° = 8°42'44″ = 0.15220573538 rad
Angle ∠ B = β = 8.71222446146° = 8°42'44″ = 0.15220573538 rad
Angle ∠ C = γ = 162.5765510771° = 162°34'32″ = 2.83774779461 rad

Height: ha = 1.55771328454
Height: hb = 1.55771328454
Height: hc = 0.78876547467

Median: ma = 7.72200518133
Median: mb = 7.72200518133
Median: mc = 0.78876547467

Inradius: r = 0.39215421081
Circumradius: R = 17.16548810048

Vertex coordinates: A[10.28; 0] B[0; 0] C[5.14; 0.78876547467]
Centroid: CG[5.14; 0.26325515822]
Coordinates of the circumscribed circle: U[5.14; -16.37772262581]
Coordinates of the inscribed circle: I[5.14; 0.39215421081]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.2887755385° = 171°17'16″ = 0.15220573538 rad
∠ B' = β' = 171.2887755385° = 171°17'16″ = 0.15220573538 rad
∠ C' = γ' = 17.42444892291° = 17°25'28″ = 2.83774779461 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 = 5.2+5.2+10.28 = 20.68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 20.68 }{ 2 } = 10.34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.34 * (10.34-5.2)(10.34-5.2)(10.34-10.28) } ; ; T = sqrt{ 16.39 } = 4.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.05 }{ 5.2 } = 1.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.05 }{ 5.2 } = 1.56 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.05 }{ 10.28 } = 0.79 ; ;

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{ 5.2**2+10.28**2-5.2**2 }{ 2 * 5.2 * 10.28 } ) = 8° 42'44" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.2**2+10.28**2-5.2**2 }{ 2 * 5.2 * 10.28 } ) = 8° 42'44" ; ; gamma = 180° - alpha - beta = 180° - 8° 42'44" - 8° 42'44" = 162° 34'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.05 }{ 10.34 } = 0.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.2 }{ 2 * sin 8° 42'44" } = 17.16 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.2**2+2 * 10.28**2 - 5.2**2 } }{ 2 } = 7.72 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.28**2+2 * 5.2**2 - 5.2**2 } }{ 2 } = 7.72 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.2**2+2 * 5.2**2 - 10.28**2 } }{ 2 } = 0.788 ; ;
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