11 16 23 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 16   c = 23

Area: T = 79.37325393319
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 25.55546937848° = 25°33'17″ = 0.44660135459 rad
Angle ∠ B = β = 38.86223042378° = 38°51'44″ = 0.67882751639 rad
Angle ∠ C = γ = 115.5833001977° = 115°34'59″ = 2.01773039438 rad

Height: ha = 14.43113707876
Height: hb = 9.92215674165
Height: hc = 6.90219599419

Median: ma = 19.03328663107
Median: mb = 16.15554944214
Median: mc = 7.5

Inradius: r = 3.17549015733
Circumradius: R = 12.75500015562

Vertex coordinates: A[23; 0] B[0; 0] C[8.56552173913; 6.90219599419]
Centroid: CG[10.52217391304; 2.3010653314]
Coordinates of the circumscribed circle: U[11.5; -5.50656824902]
Coordinates of the inscribed circle: I[9; 3.17549015733]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.4455306215° = 154°26'43″ = 0.44660135459 rad
∠ B' = β' = 141.1387695762° = 141°8'16″ = 0.67882751639 rad
∠ C' = γ' = 64.41769980226° = 64°25'1″ = 2.01773039438 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 = 11 ; ; b = 16 ; ; c = 23 ; ;

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

p = a+b+c = 11+16+23 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-11)(25-16)(25-23) } ; ; T = sqrt{ 6300 } = 79.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 79.37 }{ 11 } = 14.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 79.37 }{ 16 } = 9.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 79.37 }{ 23 } = 6.9 ; ;

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{ 11**2-16**2-23**2 }{ 2 * 16 * 23 } ) = 25° 33'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-11**2-23**2 }{ 2 * 11 * 23 } ) = 38° 51'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-11**2-16**2 }{ 2 * 16 * 11 } ) = 115° 34'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 79.37 }{ 25 } = 3.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 25° 33'17" } = 12.75 ; ;




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