5 18 19 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 18   c = 19

Area: T = 44.98998886413
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 15.22327570342° = 15°13'22″ = 0.26656872315 rad
Angle ∠ B = β = 70.95546892365° = 70°57'17″ = 1.23883929469 rad
Angle ∠ C = γ = 93.82325537293° = 93°49'21″ = 1.63875124752 rad

Height: ha = 17.96599554565
Height: hb = 4.98988765157
Height: hc = 4.72663040675

Median: ma = 18.33771208209
Median: mb = 10.58330052443
Median: mc = 9.17987798753

Inradius: r = 2.13880899353
Circumradius: R = 9.52111817431

Vertex coordinates: A[19; 0] B[0; 0] C[1.63215789474; 4.72663040675]
Centroid: CG[6.87771929825; 1.57554346892]
Coordinates of the circumscribed circle: U[9.5; -0.63547454495]
Coordinates of the inscribed circle: I[3; 2.13880899353]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.7777242966° = 164°46'38″ = 0.26656872315 rad
∠ B' = β' = 109.0455310763° = 109°2'43″ = 1.23883929469 rad
∠ C' = γ' = 86.17774462707° = 86°10'39″ = 1.63875124752 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 = 5 ; ; b = 18 ; ; c = 19 ; ;

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

p = a+b+c = 5+18+19 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-5)(21-18)(21-19) } ; ; T = sqrt{ 2016 } = 44.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.9 }{ 5 } = 17.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.9 }{ 18 } = 4.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.9 }{ 19 } = 4.73 ; ;

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{ 5**2-18**2-19**2 }{ 2 * 18 * 19 } ) = 15° 13'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-5**2-19**2 }{ 2 * 5 * 19 } ) = 70° 57'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-5**2-18**2 }{ 2 * 18 * 5 } ) = 93° 49'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.9 }{ 21 } = 2.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 15° 13'22" } = 9.52 ; ;




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