4 18 20 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 18   c = 20

Area: T = 32.72661363439
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 10.47553138432° = 10°28'31″ = 0.18328287167 rad
Angle ∠ B = β = 54.99003678046° = 54°54'1″ = 0.95881921787 rad
Angle ∠ C = γ = 114.6244318352° = 114°37'28″ = 2.00105717581 rad

Height: ha = 16.3633068172
Height: hb = 3.63662373715
Height: hc = 3.27326136344

Median: ma = 18.92108879284
Median: mb = 11.26994276696
Median: mc = 8.36766002653

Inradius: r = 1.55883874449
Circumradius: R = 111.0003819643

Vertex coordinates: A[20; 0] B[0; 0] C[2.3; 3.27326136344]
Centroid: CG[7.43333333333; 1.09108712115]
Coordinates of the circumscribed circle: U[10; -4.58334924851]
Coordinates of the inscribed circle: I[3; 1.55883874449]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.5254686157° = 169°31'29″ = 0.18328287167 rad
∠ B' = β' = 125.1099632195° = 125°5'59″ = 0.95881921787 rad
∠ C' = γ' = 65.37656816478° = 65°22'32″ = 2.00105717581 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 = 18 ; ; c = 20 ; ;

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

p = a+b+c = 4+18+20 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-4)(21-18)(21-20) } ; ; T = sqrt{ 1071 } = 32.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 32.73 }{ 4 } = 16.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 32.73 }{ 18 } = 3.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 32.73 }{ 20 } = 3.27 ; ;

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**2-18**2-20**2 }{ 2 * 18 * 20 } ) = 10° 28'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-4**2-20**2 }{ 2 * 4 * 20 } ) = 54° 54'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-4**2-18**2 }{ 2 * 18 * 4 } ) = 114° 37'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 32.73 }{ 21 } = 1.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 10° 28'31" } = 11 ; ;




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