18.5 19.2 27.5 triangle

Obtuse scalene triangle.

Sides: a = 18.5   b = 19.2   c = 27.5

Area: T = 177.2387593078
Perimeter: p = 65.2
Semiperimeter: s = 32.6

Angle ∠ A = α = 42.17216935138° = 42°10'18″ = 0.7366034903 rad
Angle ∠ B = β = 44.16774030772° = 44°10'3″ = 0.77108666058 rad
Angle ∠ C = γ = 93.66109034091° = 93°39'39″ = 1.63546911449 rad

Height: ha = 19.16108208733
Height: hb = 18.46222492789
Height: hc = 12.89900067693

Median: ma = 21.83876395245
Median: mb = 21.3879663234
Median: mc = 12.89989340645

Inradius: r = 5.4376735984
Circumradius: R = 13.77881153399

Vertex coordinates: A[27.5; 0] B[0; 0] C[13.27701818182; 12.89900067693]
Centroid: CG[13.59900606061; 4.29766689231]
Coordinates of the circumscribed circle: U[13.75; -0.88797512835]
Coordinates of the inscribed circle: I[13.4; 5.4376735984]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.8288306486° = 137°49'42″ = 0.7366034903 rad
∠ B' = β' = 135.8332596923° = 135°49'57″ = 0.77108666058 rad
∠ C' = γ' = 86.33990965909° = 86°20'21″ = 1.63546911449 rad

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How did we calculate this triangle?

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

p = a+b+c = 18.5+19.2+27.5 = 65.2 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65.2 }{ 2 } = 32.6 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.6 * (32.6-18.5)(32.6-19.2)(32.6-27.5) } ; ; T = sqrt{ 31413.16 } = 177.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 177.24 }{ 18.5 } = 19.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 177.24 }{ 19.2 } = 18.46 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 177.24 }{ 27.5 } = 12.89 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 19.2**2+27.5**2-18.5**2 }{ 2 * 19.2 * 27.5 } ) = 42° 10'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 18.5**2+27.5**2-19.2**2 }{ 2 * 18.5 * 27.5 } ) = 44° 10'3" ; ; gamma = 180° - alpha - beta = 180° - 42° 10'18" - 44° 10'3" = 93° 39'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 177.24 }{ 32.6 } = 5.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 18.5 }{ 2 * sin 42° 10'18" } = 13.78 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 19.2**2+2 * 27.5**2 - 18.5**2 } }{ 2 } = 21.838 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 27.5**2+2 * 18.5**2 - 19.2**2 } }{ 2 } = 21.38 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 19.2**2+2 * 18.5**2 - 27.5**2 } }{ 2 } = 12.899 ; ;
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