18 23 30 triangle

Obtuse scalene triangle.

Sides: a = 18   b = 23   c = 30

Area: T = 206.6666246639
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 36.80106440229° = 36°48'2″ = 0.64222924051 rad
Angle ∠ B = β = 49.94553102552° = 49°56'43″ = 0.87217101099 rad
Angle ∠ C = γ = 93.25440457219° = 93°15'15″ = 1.62875901387 rad

Height: ha = 22.96329162933
Height: hb = 17.97109779686
Height: hc = 13.7787749776

Median: ma = 25.16994258973
Median: mb = 21.90331961138
Median: mc = 14.19550695666

Inradius: r = 5.82215844124
Circumradius: R = 15.02442240835

Vertex coordinates: A[30; 0] B[0; 0] C[11.58333333333; 13.7787749776]
Centroid: CG[13.86111111111; 4.59325832587]
Coordinates of the circumscribed circle: U[15; -0.85328243139]
Coordinates of the inscribed circle: I[12.5; 5.82215844124]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1999355977° = 143°11'58″ = 0.64222924051 rad
∠ B' = β' = 130.0554689745° = 130°3'17″ = 0.87217101099 rad
∠ C' = γ' = 86.74659542781° = 86°44'45″ = 1.62875901387 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 = 18 ; ; b = 23 ; ; c = 30 ; ;

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

p = a+b+c = 18+23+30 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-18)(35.5-23)(35.5-30) } ; ; T = sqrt{ 42710.94 } = 206.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 206.67 }{ 18 } = 22.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 206.67 }{ 23 } = 17.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 206.67 }{ 30 } = 13.78 ; ;

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{ 18**2-23**2-30**2 }{ 2 * 23 * 30 } ) = 36° 48'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-18**2-30**2 }{ 2 * 18 * 30 } ) = 49° 56'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-18**2-23**2 }{ 2 * 23 * 18 } ) = 93° 15'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 206.67 }{ 35.5 } = 5.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 36° 48'2" } = 15.02 ; ;




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