4 20 22 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 20   c = 22

Area: T = 36.20877339805
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 9.47328720666° = 9°28'22″ = 0.16553328072 rad
Angle ∠ B = β = 55.37664645208° = 55°22'35″ = 0.9676501634 rad
Angle ∠ C = γ = 115.1510663413° = 115°9'2″ = 2.01097582124 rad

Height: ha = 18.10438669902
Height: hb = 3.6210773398
Height: hc = 3.292161218

Median: ma = 20.92884495365
Median: mb = 12.24774487139
Median: mc = 9.32773790531

Inradius: r = 1.57442493035
Circumradius: R = 12.15220998867

Vertex coordinates: A[22; 0] B[0; 0] C[2.27327272727; 3.292161218]
Centroid: CG[8.09109090909; 1.097720406]
Coordinates of the circumscribed circle: U[11; -5.16546424518]
Coordinates of the inscribed circle: I[3; 1.57442493035]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.5277127933° = 170°31'38″ = 0.16553328072 rad
∠ B' = β' = 124.6243535479° = 124°37'25″ = 0.9676501634 rad
∠ C' = γ' = 64.84993365875° = 64°50'58″ = 2.01097582124 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 = 4 ; ; b = 20 ; ; c = 22 ; ;

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

p = a+b+c = 4+20+22 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-4)(23-20)(23-22) } ; ; T = sqrt{ 1311 } = 36.21 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36.21 }{ 4 } = 18.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36.21 }{ 20 } = 3.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36.21 }{ 22 } = 3.29 ; ;

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{ 4**2-20**2-22**2 }{ 2 * 20 * 22 } ) = 9° 28'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-4**2-22**2 }{ 2 * 4 * 22 } ) = 55° 22'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-4**2-20**2 }{ 2 * 20 * 4 } ) = 115° 9'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36.21 }{ 23 } = 1.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 9° 28'22" } = 12.15 ; ;




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