7 22 26 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 22   c = 26

Area: T = 68.1987782222
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 13.79552993996° = 13°47'43″ = 0.24107733958 rad
Angle ∠ B = β = 48.54106961042° = 48°32'27″ = 0.84771949682 rad
Angle ∠ C = γ = 117.6644004496° = 117°39'50″ = 2.05436242895 rad

Height: ha = 19.48550806349
Height: hb = 6.21997983838
Height: hc = 5.24659832478

Median: ma = 23.82875051149
Median: mb = 15.54402702679
Median: mc = 9.87442088291

Inradius: r = 2.48799193535
Circumradius: R = 14.67878966615

Vertex coordinates: A[26; 0] B[0; 0] C[4.63546153846; 5.24659832478]
Centroid: CG[10.21215384615; 1.74986610826]
Coordinates of the circumscribed circle: U[13; -6.81547377357]
Coordinates of the inscribed circle: I[5.5; 2.48799193535]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.20547006° = 166°12'17″ = 0.24107733958 rad
∠ B' = β' = 131.4599303896° = 131°27'33″ = 0.84771949682 rad
∠ C' = γ' = 62.33659955038° = 62°20'10″ = 2.05436242895 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 = 7 ; ; b = 22 ; ; c = 26 ; ;

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

p = a+b+c = 7+22+26 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-7)(27.5-22)(27.5-26) } ; ; T = sqrt{ 4650.94 } = 68.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 68.2 }{ 7 } = 19.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 68.2 }{ 22 } = 6.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 68.2 }{ 26 } = 5.25 ; ;

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{ 7**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 13° 47'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-7**2-26**2 }{ 2 * 7 * 26 } ) = 48° 32'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-7**2-22**2 }{ 2 * 22 * 7 } ) = 117° 39'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 68.2 }{ 27.5 } = 2.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 13° 47'43" } = 14.68 ; ;




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