10 23 26 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 23   c = 26

Area: T = 114.3988153394
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 22.49549821711° = 22°29'42″ = 0.39326115041 rad
Angle ∠ B = β = 61.64106499718° = 61°38'26″ = 1.07658322951 rad
Angle ∠ C = γ = 95.8644367857° = 95°51'52″ = 1.67331488544 rad

Height: ha = 22.88796306788
Height: hb = 9.94876655125
Height: hc = 8.87998579534

Median: ma = 24.03112296814
Median: mb = 15.99221855917
Median: mc = 12.06223380818

Inradius: r = 3.87879035049
Circumradius: R = 13.06883927637

Vertex coordinates: A[26; 0] B[0; 0] C[4.75; 8.87998579534]
Centroid: CG[10.25; 2.93332859845]
Coordinates of the circumscribed circle: U[13; -1.33552488259]
Coordinates of the inscribed circle: I[6.5; 3.87879035049]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.5055017829° = 157°30'18″ = 0.39326115041 rad
∠ B' = β' = 118.3599350028° = 118°21'34″ = 1.07658322951 rad
∠ C' = γ' = 84.1365632143° = 84°8'8″ = 1.67331488544 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 = 23 ; ; c = 26 ; ;

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

p = a+b+c = 10+23+26 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-10)(29.5-23)(29.5-26) } ; ; T = sqrt{ 13086.94 } = 114.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 114.4 }{ 10 } = 22.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 114.4 }{ 23 } = 9.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 114.4 }{ 26 } = 8.8 ; ;

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**2-23**2-26**2 }{ 2 * 23 * 26 } ) = 22° 29'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-10**2-26**2 }{ 2 * 10 * 26 } ) = 61° 38'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-10**2-23**2 }{ 2 * 23 * 10 } ) = 95° 51'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 114.4 }{ 29.5 } = 3.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 22° 29'42" } = 13.07 ; ;




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