19 20 26 triangle

Acute scalene triangle.

Sides: a = 19   b = 20   c = 26

Area: T = 188.8087938128
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 46.56774634422° = 46°34'3″ = 0.81327555614 rad
Angle ∠ B = β = 49.85440523379° = 49°51'15″ = 0.87701173588 rad
Angle ∠ C = γ = 83.57884842199° = 83°34'43″ = 1.45987197335 rad

Height: ha = 19.87545198029
Height: hb = 18.88107938128
Height: hc = 14.52436875483

Median: ma = 21.16601039695
Median: mb = 20.45772725455
Median: mc = 14.54330395722

Inradius: r = 5.80994750193
Circumradius: R = 13.08220770805

Vertex coordinates: A[26; 0] B[0; 0] C[12.25; 14.52436875483]
Centroid: CG[12.75; 4.84112291828]
Coordinates of the circumscribed circle: U[13; 1.46331270419]
Coordinates of the inscribed circle: I[12.5; 5.80994750193]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.4332536558° = 133°25'57″ = 0.81327555614 rad
∠ B' = β' = 130.1465947662° = 130°8'45″ = 0.87701173588 rad
∠ C' = γ' = 96.42215157801° = 96°25'17″ = 1.45987197335 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 = 20 ; ; c = 26 ; ;

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

p = a+b+c = 19+20+26 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-19)(32.5-20)(32.5-26) } ; ; T = sqrt{ 35648.44 } = 188.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 188.81 }{ 19 } = 19.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 188.81 }{ 20 } = 18.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 188.81 }{ 26 } = 14.52 ; ;

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**2-20**2-26**2 }{ 2 * 20 * 26 } ) = 46° 34'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-19**2-26**2 }{ 2 * 19 * 26 } ) = 49° 51'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-19**2-20**2 }{ 2 * 20 * 19 } ) = 83° 34'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 188.81 }{ 32.5 } = 5.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 46° 34'3" } = 13.08 ; ;




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