11 12 17 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 12   c = 17

Area: T = 65.72767069006
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 40.11991668984° = 40°7'9″ = 0.77002115555 rad
Angle ∠ B = β = 44.66549245311° = 44°39'54″ = 0.78795499932 rad
Angle ∠ C = γ = 95.21659085705° = 95°12'57″ = 1.66218311048 rad

Height: ha = 11.95503103456
Height: hb = 10.95444511501
Height: hc = 7.7332553753

Median: ma = 13.6477344064
Median: mb = 13
Median: mc = 7.76220873481

Inradius: r = 3.2866335345
Circumradius: R = 8.53553431878

Vertex coordinates: A[17; 0] B[0; 0] C[7.82435294118; 7.7332553753]
Centroid: CG[8.27545098039; 2.57875179177]
Coordinates of the circumscribed circle: U[8.5; -0.77659402898]
Coordinates of the inscribed circle: I[8; 3.2866335345]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.8810833102° = 139°52'51″ = 0.77002115555 rad
∠ B' = β' = 135.3355075469° = 135°20'6″ = 0.78795499932 rad
∠ C' = γ' = 84.78440914295° = 84°47'3″ = 1.66218311048 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 = 12 ; ; c = 17 ; ;

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

p = a+b+c = 11+12+17 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-11)(20-12)(20-17) } ; ; T = sqrt{ 4320 } = 65.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 65.73 }{ 11 } = 11.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 65.73 }{ 12 } = 10.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 65.73 }{ 17 } = 7.73 ; ;

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**2-12**2-17**2 }{ 2 * 12 * 17 } ) = 40° 7'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-11**2-17**2 }{ 2 * 11 * 17 } ) = 44° 39'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-11**2-12**2 }{ 2 * 12 * 11 } ) = 95° 12'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 65.73 }{ 20 } = 3.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 40° 7'9" } = 8.54 ; ;




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