19 26 28 triangle

Acute scalene triangle.

Sides: a = 19   b = 26   c = 28

Area: T = 238.7644397472
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 40.99114308137° = 40°59'29″ = 0.71554354328 rad
Angle ∠ B = β = 63.84657364853° = 63°50'45″ = 1.1144318315 rad
Angle ∠ C = γ = 75.1632832701° = 75°9'46″ = 1.31218389058 rad

Height: ha = 25.13330944707
Height: hb = 18.36664921132
Height: hc = 17.05545998194

Median: ma = 25.29332797399
Median: mb = 20.08773094266
Median: mc = 17.95882849961

Inradius: r = 6.54114903417
Circumradius: R = 14.48328962635

Vertex coordinates: A[28; 0] B[0; 0] C[8.375; 17.05545998194]
Centroid: CG[12.125; 5.68548666065]
Coordinates of the circumscribed circle: U[14; 3.70986768772]
Coordinates of the inscribed circle: I[10.5; 6.54114903417]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.0098569186° = 139°31″ = 0.71554354328 rad
∠ B' = β' = 116.1544263515° = 116°9'15″ = 1.1144318315 rad
∠ C' = γ' = 104.8377167299° = 104°50'14″ = 1.31218389058 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 = 26 ; ; c = 28 ; ;

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

p = a+b+c = 19+26+28 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-19)(36.5-26)(36.5-28) } ; ; T = sqrt{ 57008.44 } = 238.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 238.76 }{ 19 } = 25.13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 238.76 }{ 26 } = 18.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 238.76 }{ 28 } = 17.05 ; ;

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**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 40° 59'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-19**2-28**2 }{ 2 * 19 * 28 } ) = 63° 50'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-19**2-26**2 }{ 2 * 26 * 19 } ) = 75° 9'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 238.76 }{ 36.5 } = 6.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 40° 59'29" } = 14.48 ; ;




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