17 18 23 triangle

Acute scalene triangle.

Sides: a = 17   b = 18   c = 23

Area: T = 151.5521971284
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 47.0665689197° = 47°3'56″ = 0.82114512412 rad
Angle ∠ B = β = 50.82333410331° = 50°49'24″ = 0.88770346379 rad
Angle ∠ C = γ = 82.11109697699° = 82°6'39″ = 1.43331067745 rad

Height: ha = 17.83296436804
Height: hb = 16.83991079204
Height: hc = 13.17884322855

Median: ma = 18.82215302247
Median: mb = 18.11107702763
Median: mc = 13.22003787824

Inradius: r = 5.22659300443
Circumradius: R = 11.61098786779

Vertex coordinates: A[23; 0] B[0; 0] C[10.73991304348; 13.17884322855]
Centroid: CG[11.24663768116; 4.39328107618]
Coordinates of the circumscribed circle: U[11.5; 1.59435127597]
Coordinates of the inscribed circle: I[11; 5.22659300443]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.9344310803° = 132°56'4″ = 0.82114512412 rad
∠ B' = β' = 129.1776658967° = 129°10'36″ = 0.88770346379 rad
∠ C' = γ' = 97.88990302301° = 97°53'21″ = 1.43331067745 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 = 17 ; ; b = 18 ; ; c = 23 ; ;

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

p = a+b+c = 17+18+23 = 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 * (29-17)(29-18)(29-23) } ; ; T = sqrt{ 22968 } = 151.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 151.55 }{ 17 } = 17.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 151.55 }{ 18 } = 16.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 151.55 }{ 23 } = 13.18 ; ;

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{ 17**2-18**2-23**2 }{ 2 * 18 * 23 } ) = 47° 3'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-17**2-23**2 }{ 2 * 17 * 23 } ) = 50° 49'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-17**2-18**2 }{ 2 * 18 * 17 } ) = 82° 6'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 151.55 }{ 29 } = 5.23 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 47° 3'56" } = 11.61 ; ;




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