5 24 26 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 24   c = 26

Area: T = 56.99550655759
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 10.52656968806° = 10°31'33″ = 0.18437080666 rad
Angle ∠ B = β = 61.26443462551° = 61°15'52″ = 1.06992645562 rad
Angle ∠ C = γ = 108.2109956864° = 108°12'36″ = 1.88986200307 rad

Height: ha = 22.79880262304
Height: hb = 4.7549588798
Height: hc = 4.38442358135

Median: ma = 24.8954778569
Median: mb = 14.37701078632
Median: mc = 11.46773449412

Inradius: r = 2.07325478391
Circumradius: R = 13.68553952552

Vertex coordinates: A[26; 0] B[0; 0] C[2.40438461538; 4.38442358135]
Centroid: CG[9.46879487179; 1.46114119378]
Coordinates of the circumscribed circle: U[13; -4.27766860172]
Coordinates of the inscribed circle: I[3.5; 2.07325478391]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.4744303119° = 169°28'27″ = 0.18437080666 rad
∠ B' = β' = 118.7365653745° = 118°44'8″ = 1.06992645562 rad
∠ C' = γ' = 71.79900431357° = 71°47'24″ = 1.88986200307 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 = 5 ; ; b = 24 ; ; c = 26 ; ;

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

p = a+b+c = 5+24+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 * (27.5-5)(27.5-24)(27.5-26) } ; ; T = sqrt{ 3248.44 } = 57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 57 }{ 5 } = 22.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 57 }{ 24 } = 4.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 57 }{ 26 } = 4.38 ; ;

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{ 5**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 10° 31'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-5**2-26**2 }{ 2 * 5 * 26 } ) = 61° 15'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-5**2-24**2 }{ 2 * 24 * 5 } ) = 108° 12'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 57 }{ 27.5 } = 2.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 10° 31'33" } = 13.69 ; ;




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