10 26 29 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 26   c = 29

Area: T = 128.9880376414
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 20.00662724699° = 20°23″ = 0.34991753257 rad
Angle ∠ B = β = 62.81329717487° = 62°48'47″ = 1.096629317 rad
Angle ∠ C = γ = 97.18107557815° = 97°10'51″ = 1.6966124158 rad

Height: ha = 25.79660752829
Height: hb = 9.92215674165
Height: hc = 8.89551983734

Median: ma = 27.08332051279
Median: mb = 17.36437553542
Median: mc = 13.3322291626

Inradius: r = 3.96986269666
Circumradius: R = 14.61546262897

Vertex coordinates: A[29; 0] B[0; 0] C[4.56989655172; 8.89551983734]
Centroid: CG[11.19896551724; 2.96550661245]
Coordinates of the circumscribed circle: U[14.5; -1.82768282862]
Coordinates of the inscribed circle: I[6.5; 3.96986269666]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.994372753° = 159°59'37″ = 0.34991753257 rad
∠ B' = β' = 117.1877028251° = 117°11'13″ = 1.096629317 rad
∠ C' = γ' = 82.81992442185° = 82°49'9″ = 1.6966124158 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 = 10 ; ; b = 26 ; ; c = 29 ; ;

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

p = a+b+c = 10+26+29 = 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 * (32.5-10)(32.5-26)(32.5-29) } ; ; T = sqrt{ 16635.94 } = 128.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 128.98 }{ 10 } = 25.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 128.98 }{ 26 } = 9.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 128.98 }{ 29 } = 8.9 ; ;

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{ 10**2-26**2-29**2 }{ 2 * 26 * 29 } ) = 20° 23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-10**2-29**2 }{ 2 * 10 * 29 } ) = 62° 48'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-10**2-26**2 }{ 2 * 26 * 10 } ) = 97° 10'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 128.98 }{ 32.5 } = 3.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 20° 23" } = 14.61 ; ;




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