7 23 26 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 23   c = 26

Area: T = 76.68111580507
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 14.86600385194° = 14°51'36″ = 0.25993565991 rad
Angle ∠ B = β = 57.42110296072° = 57°25'16″ = 1.00221860265 rad
Angle ∠ C = γ = 107.7198931873° = 107°43'8″ = 1.88800500279 rad

Height: ha = 21.90989023002
Height: hb = 6.6687926787
Height: hc = 5.89985506193

Median: ma = 24.29550612265
Median: mb = 15.17439909055
Median: mc = 10.95444511501

Inradius: r = 2.73986127875
Circumradius: R = 13.64774203912

Vertex coordinates: A[26; 0] B[0; 0] C[3.76992307692; 5.89985506193]
Centroid: CG[9.92330769231; 1.96661835398]
Coordinates of the circumscribed circle: U[13; -4.15435627277]
Coordinates of the inscribed circle: I[5; 2.73986127875]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.1439961481° = 165°8'24″ = 0.25993565991 rad
∠ B' = β' = 122.5798970393° = 122°34'44″ = 1.00221860265 rad
∠ C' = γ' = 72.28110681266° = 72°16'52″ = 1.88800500279 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 = 23 ; ; c = 26 ; ;

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

p = a+b+c = 7+23+26 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-7)(28-23)(28-26) } ; ; T = sqrt{ 5880 } = 76.68 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 76.68 }{ 7 } = 21.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 76.68 }{ 23 } = 6.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 76.68 }{ 26 } = 5.9 ; ;

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{ 7**2-23**2-26**2 }{ 2 * 23 * 26 } ) = 14° 51'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-7**2-26**2 }{ 2 * 7 * 26 } ) = 57° 25'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-7**2-23**2 }{ 2 * 23 * 7 } ) = 107° 43'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 76.68 }{ 28 } = 2.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 14° 51'36" } = 13.65 ; ;




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