22.24 18.8 3.87 triangle

Obtuse scalene triangle.

Sides: a = 22.24   b = 18.8   c = 3.87

Area: T = 18.10992612072
Perimeter: p = 44.91
Semiperimeter: s = 22.455

Angle ∠ A = α = 150.1454912661° = 150°8'42″ = 2.62105230811 rad
Angle ∠ B = β = 24.88656711975° = 24°53'8″ = 0.4344336899 rad
Angle ∠ C = γ = 4.96994161417° = 4°58'10″ = 0.08767326736 rad

Height: ha = 1.62985306841
Height: hb = 1.92765171497
Height: hc = 9.35987913215

Median: ma = 7.7821648283
Median: mb = 12.90110561583
Median: mc = 20.50108432753

Inradius: r = 0.80664689916
Circumradius: R = 22.33879272833

Vertex coordinates: A[3.87; 0] B[0; 0] C[20.175; 9.35987913215]
Centroid: CG[8.015; 3.12195971072]
Coordinates of the circumscribed circle: U[1.935; 22.25439607781]
Coordinates of the inscribed circle: I[3.655; 0.80664689916]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 29.85550873391° = 29°51'18″ = 2.62105230811 rad
∠ B' = β' = 155.1144328803° = 155°6'52″ = 0.4344336899 rad
∠ C' = γ' = 175.0310583858° = 175°1'50″ = 0.08767326736 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 = 22.24 ; ; b = 18.8 ; ; c = 3.87 ; ;

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

p = a+b+c = 22.24+18.8+3.87 = 44.91 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44.91 }{ 2 } = 22.46 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.46 * (22.46-22.24)(22.46-18.8)(22.46-3.87) } ; ; T = sqrt{ 327.95 } = 18.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18.11 }{ 22.24 } = 1.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18.11 }{ 18.8 } = 1.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18.11 }{ 3.87 } = 9.36 ; ;

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{ 18.8**2+3.87**2-22.24**2 }{ 2 * 18.8 * 3.87 } ) = 150° 8'42" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 22.24**2+3.87**2-18.8**2 }{ 2 * 22.24 * 3.87 } ) = 24° 53'8" ; ;
 gamma = 180° - alpha - beta = 180° - 150° 8'42" - 24° 53'8" = 4° 58'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18.11 }{ 22.46 } = 0.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 22.24 }{ 2 * sin 150° 8'42" } = 22.34 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 18.8**2+2 * 3.87**2 - 22.24**2 } }{ 2 } = 7.782 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.87**2+2 * 22.24**2 - 18.8**2 } }{ 2 } = 12.901 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 18.8**2+2 * 22.24**2 - 3.87**2 } }{ 2 } = 20.501 ; ;
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