8 18 19 triangle

Acute scalene triangle.

Sides: a = 8   b = 18   c = 19

Area: T = 71.68328954493
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 24.7843978051° = 24°47'2″ = 0.43325620187 rad
Angle ∠ B = β = 70.59554009401° = 70°35'43″ = 1.23221221832 rad
Angle ∠ C = γ = 84.62106210089° = 84°37'14″ = 1.47769084517 rad

Height: ha = 17.92107238623
Height: hb = 7.9654766161
Height: hc = 7.5465567942

Median: ma = 18.06993109996
Median: mb = 11.46773449412
Median: mc = 10.18657743937

Inradius: r = 3.18659064644
Circumradius: R = 9.54220252727

Vertex coordinates: A[19; 0] B[0; 0] C[2.65878947368; 7.5465567942]
Centroid: CG[7.21992982456; 2.5155189314]
Coordinates of the circumscribed circle: U[9.5; 0.89545648693]
Coordinates of the inscribed circle: I[4.5; 3.18659064644]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.2166021949° = 155°12'58″ = 0.43325620187 rad
∠ B' = β' = 109.405459906° = 109°24'17″ = 1.23221221832 rad
∠ C' = γ' = 95.37993789911° = 95°22'46″ = 1.47769084517 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 = 8 ; ; b = 18 ; ; c = 19 ; ;

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

p = a+b+c = 8+18+19 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-8)(22.5-18)(22.5-19) } ; ; T = sqrt{ 5138.44 } = 71.68 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 71.68 }{ 8 } = 17.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 71.68 }{ 18 } = 7.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 71.68 }{ 19 } = 7.55 ; ;

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{ 8**2-18**2-19**2 }{ 2 * 18 * 19 } ) = 24° 47'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-8**2-19**2 }{ 2 * 8 * 19 } ) = 70° 35'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-8**2-18**2 }{ 2 * 18 * 8 } ) = 84° 37'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 71.68 }{ 22.5 } = 3.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 24° 47'2" } = 9.54 ; ;




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