5 26 28 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 26   c = 28

Area: T = 61.59990056738
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 9.74329385734° = 9°44'35″ = 0.17700463569 rad
Angle ∠ B = β = 61.64106499718° = 61°38'26″ = 1.07658322951 rad
Angle ∠ C = γ = 108.6166411455° = 108°36'59″ = 1.89657140016 rad

Height: ha = 24.64396022695
Height: hb = 4.73883850518
Height: hc = 4.43999289767

Median: ma = 26.90326021046
Median: mb = 15.34660092532
Median: mc = 12.43298028947

Inradius: r = 2.08881018872
Circumradius: R = 14.77329657329

Vertex coordinates: A[28; 0] B[0; 0] C[2.375; 4.43999289767]
Centroid: CG[10.125; 1.46766429922]
Coordinates of the circumscribed circle: U[14; -4.71659852147]
Coordinates of the inscribed circle: I[3.5; 2.08881018872]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.2577061427° = 170°15'25″ = 0.17700463569 rad
∠ B' = β' = 118.3599350028° = 118°21'34″ = 1.07658322951 rad
∠ C' = γ' = 71.38435885453° = 71°23'1″ = 1.89657140016 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 = 26 ; ; c = 28 ; ;

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

p = a+b+c = 5+26+28 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-5)(29.5-26)(29.5-28) } ; ; T = sqrt{ 3794.44 } = 61.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 61.6 }{ 5 } = 24.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 61.6 }{ 26 } = 4.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 61.6 }{ 28 } = 4.4 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 26**2+28**2-5**2 }{ 2 * 26 * 28 } ) = 9° 44'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5**2+28**2-26**2 }{ 2 * 5 * 28 } ) = 61° 38'26" ; ; gamma = 180° - alpha - beta = 180° - 9° 44'35" - 61° 38'26" = 108° 36'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 61.6 }{ 29.5 } = 2.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5 }{ 2 * sin 9° 44'35" } = 14.77 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 28**2 - 5**2 } }{ 2 } = 26.903 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 5**2 - 26**2 } }{ 2 } = 15.346 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 5**2 - 28**2 } }{ 2 } = 12.43 ; ;
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