5 26 30 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 26   c = 30

Area: T = 41.83222543022
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 6.15875167571° = 6°9'27″ = 0.10774689412 rad
Angle ∠ B = β = 33.90112619969° = 33°54'5″ = 0.59216886424 rad
Angle ∠ C = γ = 139.9411221246° = 139°56'28″ = 2.442243507 rad

Height: ha = 16.73329017209
Height: hb = 3.21878657156
Height: hc = 2.78988169535

Median: ma = 27.965979256
Median: mb = 17.1321841699
Median: mc = 11.20326782512

Inradius: r = 1.37215493214
Circumradius: R = 23.30773740888

Vertex coordinates: A[30; 0] B[0; 0] C[4.15; 2.78988169535]
Centroid: CG[11.38333333333; 0.93296056512]
Coordinates of the circumscribed circle: U[15; -17.83991055526]
Coordinates of the inscribed circle: I[4.5; 1.37215493214]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.8422483243° = 173°50'33″ = 0.10774689412 rad
∠ B' = β' = 146.0998738003° = 146°5'55″ = 0.59216886424 rad
∠ C' = γ' = 40.05987787539° = 40°3'32″ = 2.442243507 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 = 30 ; ;

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

p = a+b+c = 5+26+30 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-5)(30.5-26)(30.5-30) } ; ; T = sqrt{ 1749.94 } = 41.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 41.83 }{ 5 } = 16.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 41.83 }{ 26 } = 3.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 41.83 }{ 30 } = 2.79 ; ;

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**2-30**2 }{ 2 * 26 * 30 } ) = 6° 9'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-5**2-30**2 }{ 2 * 5 * 30 } ) = 33° 54'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-5**2-26**2 }{ 2 * 26 * 5 } ) = 139° 56'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 41.83 }{ 30.5 } = 1.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 6° 9'27" } = 23.31 ; ;




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