4 18 19 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 18   c = 19

Area: T = 35.61551302118
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 12.02113180101° = 12°1'17″ = 0.21098115797 rad
Angle ∠ B = β = 69.59331433428° = 69°35'35″ = 1.21546294881 rad
Angle ∠ C = γ = 98.38655386471° = 98°23'8″ = 1.71771515857 rad

Height: ha = 17.80875651059
Height: hb = 3.95772366902
Height: hc = 3.74989610749

Median: ma = 18.3988369493
Median: mb = 10.36882206767
Median: mc = 8.93302855497

Inradius: r = 1.7377323425
Circumradius: R = 9.60326603853

Vertex coordinates: A[19; 0] B[0; 0] C[1.39547368421; 3.74989610749]
Centroid: CG[6.7988245614; 1.25496536916]
Coordinates of the circumscribed circle: U[9.5; -1.44003879728]
Coordinates of the inscribed circle: I[2.5; 1.7377323425]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.979868199° = 167°58'43″ = 0.21098115797 rad
∠ B' = β' = 110.4076856657° = 110°24'25″ = 1.21546294881 rad
∠ C' = γ' = 81.61444613529° = 81°36'52″ = 1.71771515857 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 = 4 ; ; b = 18 ; ; c = 19 ; ;

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

p = a+b+c = 4+18+19 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-4)(20.5-18)(20.5-19) } ; ; T = sqrt{ 1268.44 } = 35.62 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 35.62 }{ 4 } = 17.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 35.62 }{ 18 } = 3.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 35.62 }{ 19 } = 3.75 ; ;

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{ 4**2-18**2-19**2 }{ 2 * 18 * 19 } ) = 12° 1'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-4**2-19**2 }{ 2 * 4 * 19 } ) = 69° 35'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-4**2-18**2 }{ 2 * 18 * 4 } ) = 98° 23'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 35.62 }{ 20.5 } = 1.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 12° 1'17" } = 9.6 ; ;




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