7 19 24 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 19   c = 24

Area: T = 51.96215242271
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 13.17435511073° = 13°10'25″ = 0.2329921841 rad
Angle ∠ B = β = 38.21332107017° = 38°12'48″ = 0.66769463445 rad
Angle ∠ C = γ = 128.6133238191° = 128°36'48″ = 2.24547244681 rad

Height: ha = 14.84661497792
Height: hb = 5.47696341292
Height: hc = 4.33301270189

Median: ma = 21.36600093633
Median: mb = 14.90880515159
Median: mc = 7.81102496759

Inradius: r = 2.07884609691
Circumradius: R = 15.35875171604

Vertex coordinates: A[24; 0] B[0; 0] C[5.5; 4.33301270189]
Centroid: CG[9.83333333333; 1.4433375673]
Coordinates of the circumscribed circle: U[12; -9.58440144685]
Coordinates of the inscribed circle: I[6; 2.07884609691]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.8266448893° = 166°49'35″ = 0.2329921841 rad
∠ B' = β' = 141.7876789298° = 141°47'12″ = 0.66769463445 rad
∠ C' = γ' = 51.3876761809° = 51°23'12″ = 2.24547244681 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 = 7 ; ; b = 19 ; ; c = 24 ; ;

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

p = a+b+c = 7+19+24 = 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 * (25-7)(25-19)(25-24) } ; ; T = sqrt{ 2700 } = 51.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 51.96 }{ 7 } = 14.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 51.96 }{ 19 } = 5.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 51.96 }{ 24 } = 4.33 ; ;

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{ 7**2-19**2-24**2 }{ 2 * 19 * 24 } ) = 13° 10'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-7**2-24**2 }{ 2 * 7 * 24 } ) = 38° 12'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-7**2-19**2 }{ 2 * 19 * 7 } ) = 128° 36'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 51.96 }{ 25 } = 2.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 13° 10'25" } = 15.36 ; ;




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