5 19 23 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 19   c = 23

Area: T = 31.2765989193
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 8.23295587989° = 8°13'46″ = 0.1443632897 rad
Angle ∠ B = β = 32.95215907204° = 32°57'6″ = 0.57551137518 rad
Angle ∠ C = γ = 138.8198850481° = 138°49'8″ = 2.42328460047 rad

Height: ha = 12.51103956772
Height: hb = 3.29222093887
Height: hc = 2.72196512342

Median: ma = 20.94663600657
Median: mb = 13.66656503687
Median: mc = 7.79442286341

Inradius: r = 1.33108931571
Circumradius: R = 17.4655474765

Vertex coordinates: A[23; 0] B[0; 0] C[4.19656521739; 2.72196512342]
Centroid: CG[9.06552173913; 0.90765504114]
Coordinates of the circumscribed circle: U[11.5; -13.14550678494]
Coordinates of the inscribed circle: I[4.5; 1.33108931571]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.7770441201° = 171°46'14″ = 0.1443632897 rad
∠ B' = β' = 147.048840928° = 147°2'54″ = 0.57551137518 rad
∠ C' = γ' = 41.18111495194° = 41°10'52″ = 2.42328460047 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 = 19 ; ; c = 23 ; ;

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

p = a+b+c = 5+19+23 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-5)(23.5-19)(23.5-23) } ; ; T = sqrt{ 978.19 } = 31.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 31.28 }{ 5 } = 12.51 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 31.28 }{ 19 } = 3.29 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 31.28 }{ 23 } = 2.72 ; ;

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**2-19**2-23**2 }{ 2 * 19 * 23 } ) = 8° 13'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-5**2-23**2 }{ 2 * 5 * 23 } ) = 32° 57'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-5**2-19**2 }{ 2 * 19 * 5 } ) = 138° 49'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 31.28 }{ 23.5 } = 1.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 8° 13'46" } = 17.47 ; ;




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