5 26 27 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 26   c = 27

Area: T = 64.62219776856
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 10.60991428782° = 10°36'33″ = 0.1855164474 rad
Angle ∠ B = β = 73.20985528854° = 73°12'31″ = 1.27877302885 rad
Angle ∠ C = γ = 96.18223042364° = 96°10'56″ = 1.67986978911 rad

Height: ha = 25.84987910742
Height: hb = 4.97109213604
Height: hc = 4.78768131619

Median: ma = 26.38765496039
Median: mb = 14.42222051019
Median: mc = 12.97111217711

Inradius: r = 2.22883440581
Circumradius: R = 13.57989716042

Vertex coordinates: A[27; 0] B[0; 0] C[1.44444444444; 4.78768131619]
Centroid: CG[9.48114814815; 1.59656043873]
Coordinates of the circumscribed circle: U[13.5; -1.46223507881]
Coordinates of the inscribed circle: I[3; 2.22883440581]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.3910857122° = 169°23'27″ = 0.1855164474 rad
∠ B' = β' = 106.7911447115° = 106°47'29″ = 1.27877302885 rad
∠ C' = γ' = 83.81876957636° = 83°49'4″ = 1.67986978911 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 = 27 ; ;

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

p = a+b+c = 5+26+27 = 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 * (29-5)(29-26)(29-27) } ; ; T = sqrt{ 4176 } = 64.62 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 64.62 }{ 5 } = 25.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 64.62 }{ 26 } = 4.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 64.62 }{ 27 } = 4.79 ; ;

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**2-26**2-27**2 }{ 2 * 26 * 27 } ) = 10° 36'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-5**2-27**2 }{ 2 * 5 * 27 } ) = 73° 12'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-5**2-26**2 }{ 2 * 26 * 5 } ) = 96° 10'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 64.62 }{ 29 } = 2.23 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 10° 36'33" } = 13.58 ; ;




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