22 26 29 triangle

Acute scalene triangle.

Sides: a = 22   b = 26   c = 29

Area: T = 274.6566034887
Perimeter: p = 77
Semiperimeter: s = 38.5

Angle ∠ A = α = 46.76333498139° = 46°45'48″ = 0.81661744235 rad
Angle ∠ B = β = 59.42880018247° = 59°25'41″ = 1.03772142997 rad
Angle ∠ C = γ = 73.80986483614° = 73°48'31″ = 1.28882039304 rad

Height: ha = 24.96987304443
Height: hb = 21.1277387299
Height: hc = 18.94217955095

Median: ma = 25.24987623459
Median: mb = 22.21548598915
Median: mc = 19.2298884523

Inradius: r = 7.13439229841
Circumradius: R = 15.09988854175

Vertex coordinates: A[29; 0] B[0; 0] C[11.19896551724; 18.94217955095]
Centroid: CG[13.39765517241; 6.31439318365]
Coordinates of the circumscribed circle: U[14.5; 4.2110266126]
Coordinates of the inscribed circle: I[12.5; 7.13439229841]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.2376650186° = 133°14'12″ = 0.81661744235 rad
∠ B' = β' = 120.5721998175° = 120°34'19″ = 1.03772142997 rad
∠ C' = γ' = 106.1911351639° = 106°11'29″ = 1.28882039304 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 = 22 ; ; b = 26 ; ; c = 29 ; ;

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

p = a+b+c = 22+26+29 = 77 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 77 }{ 2 } = 38.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.5 * (38.5-22)(38.5-26)(38.5-29) } ; ; T = sqrt{ 75435.94 } = 274.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 274.66 }{ 22 } = 24.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 274.66 }{ 26 } = 21.13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 274.66 }{ 29 } = 18.94 ; ;

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{ 22**2-26**2-29**2 }{ 2 * 26 * 29 } ) = 46° 45'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 59° 25'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-22**2-26**2 }{ 2 * 26 * 22 } ) = 73° 48'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 274.66 }{ 38.5 } = 7.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 46° 45'48" } = 15.1 ; ;




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