3 18 20 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 18   c = 20

Area: T = 21.17663429326
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 6.75662861124° = 6°45'23″ = 0.11879194379 rad
Angle ∠ B = β = 44.90105279607° = 44°54'2″ = 0.78436620488 rad
Angle ∠ C = γ = 128.3433185927° = 128°20'35″ = 2.24400111669 rad

Height: ha = 14.11875619551
Height: hb = 2.35329269925
Height: hc = 2.11876342933

Median: ma = 18.96770767384
Median: mb = 11.11330553854
Median: mc = 8.15547532152

Inradius: r = 1.03329923382
Circumradius: R = 12.75500768598

Vertex coordinates: A[20; 0] B[0; 0] C[2.125; 2.11876342933]
Centroid: CG[7.375; 0.70658780978]
Coordinates of the circumscribed circle: U[10; -7.91097699038]
Coordinates of the inscribed circle: I[2.5; 1.03329923382]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.2443713888° = 173°14'37″ = 0.11879194379 rad
∠ B' = β' = 135.0999472039° = 135°5'58″ = 0.78436620488 rad
∠ C' = γ' = 51.65768140731° = 51°39'25″ = 2.24400111669 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 = 3 ; ; b = 18 ; ; c = 20 ; ;

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

p = a+b+c = 3+18+20 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-3)(20.5-18)(20.5-20) } ; ; T = sqrt{ 448.44 } = 21.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.18 }{ 3 } = 14.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.18 }{ 18 } = 2.35 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.18 }{ 20 } = 2.12 ; ;

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{ 3**2-18**2-20**2 }{ 2 * 18 * 20 } ) = 6° 45'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-3**2-20**2 }{ 2 * 3 * 20 } ) = 44° 54'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-3**2-18**2 }{ 2 * 18 * 3 } ) = 128° 20'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.18 }{ 20.5 } = 1.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 6° 45'23" } = 12.75 ; ;




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