8 24 26 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 24   c = 26

Area: T = 95.57771939324
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 17.83986287523° = 17°50'19″ = 0.31113428058 rad
Angle ∠ B = β = 66.78219922566° = 66°46'55″ = 1.16655656459 rad
Angle ∠ C = γ = 95.37993789911° = 95°22'46″ = 1.66546842019 rad

Height: ha = 23.89442984831
Height: hb = 7.9654766161
Height: hc = 7.3522091841

Median: ma = 24.69881780705
Median: mb = 15.03332963784
Median: mc = 12.28882057274

Inradius: r = 3.2965765308
Circumradius: R = 13.05875082679

Vertex coordinates: A[26; 0] B[0; 0] C[3.15438461538; 7.3522091841]
Centroid: CG[9.71879487179; 2.45106972803]
Coordinates of the circumscribed circle: U[13; -1.22441414001]
Coordinates of the inscribed circle: I[5; 3.2965765308]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.1611371248° = 162°9'41″ = 0.31113428058 rad
∠ B' = β' = 113.2188007743° = 113°13'5″ = 1.16655656459 rad
∠ C' = γ' = 84.62106210089° = 84°37'14″ = 1.66546842019 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 = 8 ; ; b = 24 ; ; c = 26 ; ;

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

p = a+b+c = 8+24+26 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-8)(29-24)(29-26) } ; ; T = sqrt{ 9135 } = 95.58 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 95.58 }{ 8 } = 23.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 95.58 }{ 24 } = 7.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 95.58 }{ 26 } = 7.35 ; ;

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{ 8**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 17° 50'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-8**2-26**2 }{ 2 * 8 * 26 } ) = 66° 46'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-8**2-24**2 }{ 2 * 24 * 8 } ) = 95° 22'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 95.58 }{ 29 } = 3.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 17° 50'19" } = 13.06 ; ;




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