11 15 20 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 15   c = 20

Area: T = 81.38879597975
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 32.86598803789° = 32°51'36″ = 0.57435131044 rad
Angle ∠ B = β = 47.72220924012° = 47°43'20″ = 0.83329076383 rad
Angle ∠ C = γ = 99.418802722° = 99°25'5″ = 1.73551719108 rad

Height: ha = 14.79878108723
Height: hb = 10.8521727973
Height: hc = 8.13987959798

Median: ma = 16.88002976164
Median: mb = 14.2921605928
Median: mc = 8.54440037453

Inradius: r = 3.53986069477
Circumradius: R = 10.13766344856

Vertex coordinates: A[20; 0] B[0; 0] C[7.4; 8.13987959798]
Centroid: CG[9.13333333333; 2.71329319933]
Coordinates of the circumscribed circle: U[10; -1.65987220067]
Coordinates of the inscribed circle: I[8; 3.53986069477]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.1440119621° = 147°8'24″ = 0.57435131044 rad
∠ B' = β' = 132.2787907599° = 132°16'40″ = 0.83329076383 rad
∠ C' = γ' = 80.582197278° = 80°34'55″ = 1.73551719108 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 = 15 ; ; c = 20 ; ;

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

p = a+b+c = 11+15+20 = 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 * (23-11)(23-15)(23-20) } ; ; T = sqrt{ 6624 } = 81.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 81.39 }{ 11 } = 14.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 81.39 }{ 15 } = 10.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 81.39 }{ 20 } = 8.14 ; ;

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**2-15**2-20**2 }{ 2 * 15 * 20 } ) = 32° 51'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-11**2-20**2 }{ 2 * 11 * 20 } ) = 47° 43'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-11**2-15**2 }{ 2 * 15 * 11 } ) = 99° 25'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 81.39 }{ 23 } = 3.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 32° 51'36" } = 10.14 ; ;




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