1.414 1.414 2.449 triangle

Obtuse isosceles triangle.

Sides: a = 1.41442135624   b = 1.41442135624   c = 2.44994897428

Area: T = 0.86660254038
Perimeter: p = 5.27879168676
Semiperimeter: s = 2.63989584338

Angle ∠ A = α = 300.0000000012° = 30° = 0.52435987756 rad
Angle ∠ B = β = 300.0000000012° = 30° = 0.52435987756 rad
Angle ∠ C = γ = 1209.999999998° = 120° = 2.09443951024 rad

Height: ha = 1.22547448714
Height: hb = 1.22547448714
Height: hc = 0.70771067812

Median: ma = 1.87108286934
Median: mb = 1.87108286934
Median: mc = 0.70771067812

Inradius: r = 0.32881693992
Circumradius: R = 1.41442135623

Vertex coordinates: A[2.44994897428; 0] B[0; 0] C[1.22547448714; 0.70771067812]
Centroid: CG[1.22547448714; 0.23657022604]
Coordinates of the circumscribed circle: U[1.22547448714; -0.70771067811]
Coordinates of the inscribed circle: I[1.22547448714; 0.32881693992]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1509.999999999° = 150° = 0.52435987756 rad
∠ B' = β' = 1509.999999999° = 150° = 0.52435987756 rad
∠ C' = γ' = 600.0000000024° = 60° = 2.09443951024 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 = 1.41+1.41+2.45 = 5.28 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 5.28 }{ 2 } = 2.64 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2.64 * (2.64-1.41)(2.64-1.41)(2.64-2.45) } ; ; T = sqrt{ 0.75 } = 0.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.87 }{ 1.41 } = 1.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.87 }{ 1.41 } = 1.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.87 }{ 2.45 } = 0.71 ; ;

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{ 1.41**2+2.45**2-1.41**2 }{ 2 * 1.41 * 2.45 } ) = 30° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1.41**2+2.45**2-1.41**2 }{ 2 * 1.41 * 2.45 } ) = 30° ; ; gamma = 180° - alpha - beta = 180° - 30° - 30° = 120° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.87 }{ 2.64 } = 0.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1.41 }{ 2 * sin 30° } = 1.41 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.41**2+2 * 2.45**2 - 1.41**2 } }{ 2 } = 1.871 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.45**2+2 * 1.41**2 - 1.41**2 } }{ 2 } = 1.871 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.41**2+2 * 1.41**2 - 2.45**2 } }{ 2 } = 0.707 ; ;
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