45.3 36.1 74.37 triangle

Obtuse scalene triangle.

Sides: a = 45.3   b = 36.1   c = 74.37

Area: T = 610.5322296664
Perimeter: p = 155.77
Semiperimeter: s = 77.885

Angle ∠ A = α = 27.05329558741° = 27°3'11″ = 0.47221631524 rad
Angle ∠ B = β = 21.25504557803° = 21°15'2″ = 0.37108904209 rad
Angle ∠ C = γ = 131.6976588346° = 131°41'48″ = 2.29985390803 rad

Height: ha = 26.95550682854
Height: hb = 33.82545039703
Height: hc = 16.41987789879

Median: ma = 53.8899061506
Median: mb = 58.87701193306
Median: mc = 17.17334031281

Inradius: r = 7.83988944811
Circumradius: R = 49.80105972676

Vertex coordinates: A[74.37; 0] B[0; 0] C[42.22198258706; 16.41987789879]
Centroid: CG[38.86332752902; 5.47329263293]
Coordinates of the circumscribed circle: U[37.185; -33.1276654875]
Coordinates of the inscribed circle: I[41.785; 7.83988944811]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.9477044126° = 152°56'49″ = 0.47221631524 rad
∠ B' = β' = 158.754954422° = 158°44'58″ = 0.37108904209 rad
∠ C' = γ' = 48.30334116544° = 48°18'12″ = 2.29985390803 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 = 45.3 ; ; b = 36.1 ; ; c = 74.37 ; ;

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

p = a+b+c = 45.3+36.1+74.37 = 155.77 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 155.77 }{ 2 } = 77.89 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 77.89 * (77.89-45.3)(77.89-36.1)(77.89-74.37) } ; ; T = sqrt{ 372749.69 } = 610.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 610.53 }{ 45.3 } = 26.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 610.53 }{ 36.1 } = 33.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 610.53 }{ 74.37 } = 16.42 ; ;

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{ 36.1**2+74.37**2-45.3**2 }{ 2 * 36.1 * 74.37 } ) = 27° 3'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 45.3**2+74.37**2-36.1**2 }{ 2 * 45.3 * 74.37 } ) = 21° 15'2" ; ;
 gamma = 180° - alpha - beta = 180° - 27° 3'11" - 21° 15'2" = 131° 41'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 610.53 }{ 77.89 } = 7.84 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 45.3 }{ 2 * sin 27° 3'11" } = 49.8 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 36.1**2+2 * 74.37**2 - 45.3**2 } }{ 2 } = 53.889 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 74.37**2+2 * 45.3**2 - 36.1**2 } }{ 2 } = 58.87 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 36.1**2+2 * 45.3**2 - 74.37**2 } }{ 2 } = 17.173 ; ;
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