922 260 885 triangle

Acute scalene triangle.

Sides: a = 922   b = 260   c = 885

Area: T = 115049.8510858
Perimeter: p = 2067
Semiperimeter: s = 1033.5

Angle ∠ A = α = 89.9087744044° = 89°54'28″ = 1.56991861566 rad
Angle ∠ B = β = 16.37993263723° = 16°22'46″ = 0.28658731745 rad
Angle ∠ C = γ = 73.71329295837° = 73°42'47″ = 1.28765333225 rad

Height: ha = 249.5665837002
Height: hb = 884.9998852754
Height: hc = 2609.999662956

Median: ma = 461.4021668831
Median: mb = 894.2989941797
Median: mc = 512.8770110262

Inradius: r = 111.3210610409
Circumradius: R = 461.0010597606

Vertex coordinates: A[885; 0] B[0; 0] C[884.5811355932; 2609.999662956]
Centroid: CG[589.8660451977; 86.66765543186]
Coordinates of the circumscribed circle: U[442.5; 129.2887667599]
Coordinates of the inscribed circle: I[773.5; 111.3210610409]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90.0922255956° = 90°5'32″ = 1.56991861566 rad
∠ B' = β' = 163.6210673628° = 163°37'14″ = 0.28658731745 rad
∠ C' = γ' = 106.2877070416° = 106°17'13″ = 1.28765333225 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 = 922 ; ; b = 260 ; ; c = 885 ; ;

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

p = a+b+c = 922+260+885 = 2067 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2067 }{ 2 } = 1033.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1033.5 * (1033.5-922)(1033.5-260)(1033.5-885) } ; ; T = sqrt{ 13236468182.4 } = 115049.85 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 115049.85 }{ 922 } = 249.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 115049.85 }{ 260 } = 885 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 115049.85 }{ 885 } = 260 ; ;

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{ 922**2-260**2-885**2 }{ 2 * 260 * 885 } ) = 89° 54'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 260**2-922**2-885**2 }{ 2 * 922 * 885 } ) = 16° 22'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 885**2-922**2-260**2 }{ 2 * 260 * 922 } ) = 73° 42'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 115049.85 }{ 1033.5 } = 111.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 922 }{ 2 * sin 89° 54'28" } = 461 ; ;




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