6 12 17 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 12   c = 17

Area: T = 23.52552523897
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 13.3354738201° = 13°20'5″ = 0.23327350865 rad
Angle ∠ B = β = 27.47696994896° = 27°28'11″ = 0.47994367006 rad
Angle ∠ C = γ = 139.1965562309° = 139°11'44″ = 2.42994208665 rad

Height: ha = 7.84217507966
Height: hb = 3.92108753983
Height: hc = 2.76876767517

Median: ma = 14.40548602909
Median: mb = 11.24772218792
Median: mc = 4.21330748866

Inradius: r = 1.34443001366
Circumradius: R = 13.0077299345

Vertex coordinates: A[17; 0] B[0; 0] C[5.32435294118; 2.76876767517]
Centroid: CG[7.44111764706; 0.92325589172]
Coordinates of the circumscribed circle: U[8.5; -9.84658029764]
Coordinates of the inscribed circle: I[5.5; 1.34443001366]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.6655261799° = 166°39'55″ = 0.23327350865 rad
∠ B' = β' = 152.533030051° = 152°31'49″ = 0.47994367006 rad
∠ C' = γ' = 40.80444376906° = 40°48'16″ = 2.42994208665 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 = 6 ; ; b = 12 ; ; c = 17 ; ;

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

p = a+b+c = 6+12+17 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-6)(17.5-12)(17.5-17) } ; ; T = sqrt{ 553.44 } = 23.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 23.53 }{ 6 } = 7.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 23.53 }{ 12 } = 3.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 23.53 }{ 17 } = 2.77 ; ;

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{ 6**2-12**2-17**2 }{ 2 * 12 * 17 } ) = 13° 20'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-6**2-17**2 }{ 2 * 6 * 17 } ) = 27° 28'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-6**2-12**2 }{ 2 * 12 * 6 } ) = 139° 11'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 23.53 }{ 17.5 } = 1.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 13° 20'5" } = 13.01 ; ;




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