0.3 0.4 0.6 triangle

Obtuse scalene triangle.

Sides: a = 0.3   b = 0.4   c = 0.6

Area: T = 0.05333268225
Perimeter: p = 1.3
Semiperimeter: s = 0.65

Angle ∠ A = α = 26.38443297494° = 26°23'4″ = 0.46604934251 rad
Angle ∠ B = β = 36.33660575146° = 36°20'10″ = 0.63441838408 rad
Angle ∠ C = γ = 117.2879612736° = 117°16'47″ = 2.04769153877 rad

Height: ha = 0.35655121501
Height: hb = 0.26766341126
Height: hc = 0.17877560751

Median: ma = 0.48773397172
Median: mb = 0.43301162634
Median: mc = 0.18770828693

Inradius: r = 0.08220412654
Circumradius: R = 0.33875412063

Vertex coordinates: A[0.6; 0] B[0; 0] C[0.24216666667; 0.17877560751]
Centroid: CG[0.28105555556; 0.0599252025]
Coordinates of the circumscribed circle: U[0.3; -0.15547063862]
Coordinates of the inscribed circle: I[0.25; 0.08220412654]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.6165670251° = 153°36'56″ = 0.46604934251 rad
∠ B' = β' = 143.6643942485° = 143°39'50″ = 0.63441838408 rad
∠ C' = γ' = 62.7220387264° = 62°43'13″ = 2.04769153877 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 0.3 ; ; b = 0.4 ; ; c = 0.6 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 0.3+0.4+0.6 = 1.3 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1.3 }{ 2 } = 0.65 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.65 * (0.65-0.3)(0.65-0.4)(0.65-0.6) } ; ; T = sqrt{ 0 } = 0.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.05 }{ 0.3 } = 0.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.05 }{ 0.4 } = 0.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.05 }{ 0.6 } = 0.18 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 0.3**2-0.4**2-0.6**2 }{ 2 * 0.4 * 0.6 } ) = 26° 23'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 0.4**2-0.3**2-0.6**2 }{ 2 * 0.3 * 0.6 } ) = 36° 20'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.6**2-0.3**2-0.4**2 }{ 2 * 0.4 * 0.3 } ) = 117° 16'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.05 }{ 0.65 } = 0.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 0.3 }{ 2 * sin 26° 23'4" } = 0.34 ; ;

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