11 17 20 triangle

Acute scalene triangle.

Sides: a = 11   b = 17   c = 20

Area: T = 93.46765715644
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 33.35435238375° = 33°21'13″ = 0.58221288081 rad
Angle ∠ B = β = 58.17986314749° = 58°10'43″ = 1.01554086735 rad
Angle ∠ C = γ = 88.46878446876° = 88°28'4″ = 1.54440551719 rad

Height: ha = 16.99439221026
Height: hb = 10.99660672429
Height: hc = 9.34766571564

Median: ma = 17.72770979012
Median: mb = 13.7220422734
Median: mc = 10.2476950766

Inradius: r = 3.89444404818
Circumradius: R = 10.00435765124

Vertex coordinates: A[20; 0] B[0; 0] C[5.8; 9.34766571564]
Centroid: CG[8.6; 3.11655523855]
Coordinates of the circumscribed circle: U[10; 0.26774753078]
Coordinates of the inscribed circle: I[7; 3.89444404818]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.6466476163° = 146°38'47″ = 0.58221288081 rad
∠ B' = β' = 121.8211368525° = 121°49'17″ = 1.01554086735 rad
∠ C' = γ' = 91.53221553124° = 91°31'56″ = 1.54440551719 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 = 11 ; ; b = 17 ; ; c = 20 ; ;

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

p = a+b+c = 11+17+20 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-11)(24-17)(24-20) } ; ; T = sqrt{ 8736 } = 93.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 93.47 }{ 11 } = 16.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 93.47 }{ 17 } = 11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 93.47 }{ 20 } = 9.35 ; ;

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{ 11**2-17**2-20**2 }{ 2 * 17 * 20 } ) = 33° 21'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-11**2-20**2 }{ 2 * 11 * 20 } ) = 58° 10'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-11**2-17**2 }{ 2 * 17 * 11 } ) = 88° 28'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 93.47 }{ 24 } = 3.89 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 33° 21'13" } = 10 ; ;




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