19 28 29 triangle

Acute scalene triangle.

Sides: a = 19   b = 28   c = 29

Area: T = 254.9121749435
Perimeter: p = 76
Semiperimeter: s = 38

Angle ∠ A = α = 38.89325199738° = 38°53'33″ = 0.67988025279 rad
Angle ∠ B = β = 67.70990296252° = 67°42'33″ = 1.18217455003 rad
Angle ∠ C = γ = 73.3988450401° = 73°23'54″ = 1.28110446254 rad

Height: ha = 26.833281573
Height: hb = 18.20879821025
Height: hc = 17.58801206507

Median: ma = 26.87547093008
Median: mb = 20.12546117975
Median: mc = 19.03328663107

Inradius: r = 6.70882039325
Circumradius: R = 15.13107266477

Vertex coordinates: A[29; 0] B[0; 0] C[7.20768965517; 17.58801206507]
Centroid: CG[12.06989655172; 5.86600402169]
Coordinates of the circumscribed circle: U[14.5; 4.32330647565]
Coordinates of the inscribed circle: I[10; 6.70882039325]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.1077480026° = 141°6'27″ = 0.67988025279 rad
∠ B' = β' = 112.2910970375° = 112°17'27″ = 1.18217455003 rad
∠ C' = γ' = 106.6021549599° = 106°36'6″ = 1.28110446254 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 = 19 ; ; b = 28 ; ; c = 29 ; ;

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

p = a+b+c = 19+28+29 = 76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 76 }{ 2 } = 38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38 * (38-19)(38-28)(38-29) } ; ; T = sqrt{ 64980 } = 254.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 254.91 }{ 19 } = 26.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 254.91 }{ 28 } = 18.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 254.91 }{ 29 } = 17.58 ; ;

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{ 19**2-28**2-29**2 }{ 2 * 28 * 29 } ) = 38° 53'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-19**2-29**2 }{ 2 * 19 * 29 } ) = 67° 42'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-19**2-28**2 }{ 2 * 28 * 19 } ) = 73° 23'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 254.91 }{ 38 } = 6.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 38° 53'33" } = 15.13 ; ;




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