17 19 29 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 19   c = 29

Area: T = 154.2879575771
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 34.05656912516° = 34°3'20″ = 0.59443839414 rad
Angle ∠ B = β = 38.74768527241° = 38°44'49″ = 0.67662601548 rad
Angle ∠ C = γ = 107.1977456024° = 107°11'51″ = 1.87109485574 rad

Height: ha = 18.1510538326
Height: hb = 16.24399553443
Height: hc = 10.64399707428

Median: ma = 22.99545645751
Median: mb = 21.78987585695
Median: mc = 10.71221426428

Inradius: r = 4.74770638699
Circumradius: R = 15.17986131657

Vertex coordinates: A[29; 0] B[0; 0] C[13.25986206897; 10.64399707428]
Centroid: CG[14.08662068966; 3.54766569143]
Coordinates of the circumscribed circle: U[14.5; -4.48877942951]
Coordinates of the inscribed circle: I[13.5; 4.74770638699]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.9444308748° = 145°56'40″ = 0.59443839414 rad
∠ B' = β' = 141.2533147276° = 141°15'11″ = 0.67662601548 rad
∠ C' = γ' = 72.80325439757° = 72°48'9″ = 1.87109485574 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 = 17 ; ; b = 19 ; ; c = 29 ; ;

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

p = a+b+c = 17+19+29 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-17)(32.5-19)(32.5-29) } ; ; T = sqrt{ 23802.19 } = 154.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 154.28 }{ 17 } = 18.15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 154.28 }{ 19 } = 16.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 154.28 }{ 29 } = 10.64 ; ;

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{ 17**2-19**2-29**2 }{ 2 * 19 * 29 } ) = 34° 3'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-17**2-29**2 }{ 2 * 17 * 29 } ) = 38° 44'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-17**2-19**2 }{ 2 * 19 * 17 } ) = 107° 11'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 154.28 }{ 32.5 } = 4.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 34° 3'20" } = 15.18 ; ;




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