15 22 26 triangle

Acute scalene triangle.

Sides: a = 15   b = 22   c = 26

Area: T = 164.7943620932
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 35.18438154883° = 35°11'2″ = 0.61440734237 rad
Angle ∠ B = β = 57.68221684943° = 57°40'56″ = 1.00767437599 rad
Angle ∠ C = γ = 87.13440160174° = 87°8'2″ = 1.521077547 rad

Height: ha = 21.9722482791
Height: hb = 14.98112382666
Height: hc = 12.67664323794

Median: ma = 22.88655849827
Median: mb = 18.15221348607
Median: mc = 13.62198384719

Inradius: r = 5.23215435217
Circumradius: R = 13.01662805324

Vertex coordinates: A[26; 0] B[0; 0] C[8.01992307692; 12.67664323794]
Centroid: CG[11.34397435897; 4.22554774598]
Coordinates of the circumscribed circle: U[13; 0.65108140266]
Coordinates of the inscribed circle: I[9.5; 5.23215435217]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.8166184512° = 144°48'58″ = 0.61440734237 rad
∠ B' = β' = 122.3187831506° = 122°19'4″ = 1.00767437599 rad
∠ C' = γ' = 92.86659839826° = 92°51'58″ = 1.521077547 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 = 15 ; ; b = 22 ; ; c = 26 ; ;

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

p = a+b+c = 15+22+26 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-15)(31.5-22)(31.5-26) } ; ; T = sqrt{ 27156.94 } = 164.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 164.79 }{ 15 } = 21.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 164.79 }{ 22 } = 14.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 164.79 }{ 26 } = 12.68 ; ;

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{ 15**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 35° 11'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-15**2-26**2 }{ 2 * 15 * 26 } ) = 57° 40'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-15**2-22**2 }{ 2 * 22 * 15 } ) = 87° 8'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 164.79 }{ 31.5 } = 5.23 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 35° 11'2" } = 13.02 ; ;




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