6 22 23 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 22   c = 23

Area: T = 65.96216365776
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 15.11326658929° = 15°6'46″ = 0.26437657786 rad
Angle ∠ B = β = 72.93436903541° = 72°56'1″ = 1.27329330323 rad
Angle ∠ C = γ = 91.95436437529° = 91°57'13″ = 1.60548938427 rad

Height: ha = 21.98772121925
Height: hb = 5.99765124161
Height: hc = 5.7365794485

Median: ma = 22.30547080232
Median: mb = 12.70882650271
Median: mc = 11.30326545555

Inradius: r = 2.58767308462
Circumradius: R = 11.50766884235

Vertex coordinates: A[23; 0] B[0; 0] C[1.76108695652; 5.7365794485]
Centroid: CG[8.25436231884; 1.9121931495]
Coordinates of the circumscribed circle: U[11.5; -0.3922273469]
Coordinates of the inscribed circle: I[3.5; 2.58767308462]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.8877334107° = 164°53'14″ = 0.26437657786 rad
∠ B' = β' = 107.0666309646° = 107°3'59″ = 1.27329330323 rad
∠ C' = γ' = 88.04663562471° = 88°2'47″ = 1.60548938427 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 = 6 ; ; b = 22 ; ; c = 23 ; ;

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

p = a+b+c = 6+22+23 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-6)(25.5-22)(25.5-23) } ; ; T = sqrt{ 4350.94 } = 65.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 65.96 }{ 6 } = 21.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 65.96 }{ 22 } = 6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 65.96 }{ 23 } = 5.74 ; ;

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{ 6**2-22**2-23**2 }{ 2 * 22 * 23 } ) = 15° 6'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-6**2-23**2 }{ 2 * 6 * 23 } ) = 72° 56'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-6**2-22**2 }{ 2 * 22 * 6 } ) = 91° 57'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 65.96 }{ 25.5 } = 2.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 15° 6'46" } = 11.51 ; ;




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