10 12 17 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 12   c = 17

Area: T = 58.93658761706
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 35.2966144734° = 35°17'46″ = 0.61660339389 rad
Angle ∠ B = β = 43.89769323912° = 43°53'49″ = 0.76661460018 rad
Angle ∠ C = γ = 100.8076922875° = 100°48'25″ = 1.7599412713 rad

Height: ha = 11.78771752341
Height: hb = 9.82326460284
Height: hc = 6.93436324907

Median: ma = 13.83883525031
Median: mb = 12.5989678312
Median: mc = 7.05333679898

Inradius: r = 3.02223526241
Circumradius: R = 8.65334727765

Vertex coordinates: A[17; 0] B[0; 0] C[7.20658823529; 6.93436324907]
Centroid: CG[8.0698627451; 2.31112108302]
Coordinates of the circumscribed circle: U[8.5; -1.62325261456]
Coordinates of the inscribed circle: I[7.5; 3.02223526241]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.7043855266° = 144°42'14″ = 0.61660339389 rad
∠ B' = β' = 136.1033067609° = 136°6'11″ = 0.76661460018 rad
∠ C' = γ' = 79.19330771251° = 79°11'35″ = 1.7599412713 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 = 10 ; ; b = 12 ; ; c = 17 ; ;

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

p = a+b+c = 10+12+17 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-10)(19.5-12)(19.5-17) } ; ; T = sqrt{ 3473.44 } = 58.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 58.94 }{ 10 } = 11.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 58.94 }{ 12 } = 9.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 58.94 }{ 17 } = 6.93 ; ;

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{ 10**2-12**2-17**2 }{ 2 * 12 * 17 } ) = 35° 17'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-10**2-17**2 }{ 2 * 10 * 17 } ) = 43° 53'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-10**2-12**2 }{ 2 * 12 * 10 } ) = 100° 48'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 58.94 }{ 19.5 } = 3.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 35° 17'46" } = 8.65 ; ;




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