8 26 28 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 26   c = 28

Area: T = 103.4176633092
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 16.50657537272° = 16°30'21″ = 0.28880797481 rad
Angle ∠ B = β = 67.42327592381° = 67°25'22″ = 1.17767491395 rad
Angle ∠ C = γ = 96.07114870347° = 96°4'17″ = 1.6776763766 rad

Height: ha = 25.85441582729
Height: hb = 7.95551256224
Height: hc = 7.38769023637

Median: ma = 26.72107784318
Median: mb = 15.96987194227
Median: mc = 13.19109059583

Inradius: r = 3.33660204223
Circumradius: R = 14.07989731446

Vertex coordinates: A[28; 0] B[0; 0] C[3.07114285714; 7.38769023637]
Centroid: CG[10.35771428571; 2.46223007879]
Coordinates of the circumscribed circle: U[14; -1.48991221595]
Coordinates of the inscribed circle: I[5; 3.33660204223]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.4944246273° = 163°29'39″ = 0.28880797481 rad
∠ B' = β' = 112.5777240762° = 112°34'38″ = 1.17767491395 rad
∠ C' = γ' = 83.92985129653° = 83°55'43″ = 1.6776763766 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 = 26 ; ; c = 28 ; ;

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

p = a+b+c = 8+26+28 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-8)(31-26)(31-28) } ; ; T = sqrt{ 10695 } = 103.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 103.42 }{ 8 } = 25.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 103.42 }{ 26 } = 7.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 103.42 }{ 28 } = 7.39 ; ;

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**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 16° 30'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-8**2-28**2 }{ 2 * 8 * 28 } ) = 67° 25'22" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-8**2-26**2 }{ 2 * 26 * 8 } ) = 96° 4'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 103.42 }{ 31 } = 3.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 16° 30'21" } = 14.08 ; ;




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