17 21 30 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 21   c = 30

Area: T = 173.3676663462
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 33.39224249359° = 33°23'33″ = 0.58328077604 rad
Angle ∠ B = β = 42.83334280661° = 42°50' = 0.74875843497 rad
Angle ∠ C = γ = 103.7744146998° = 103°46'27″ = 1.81112005436 rad

Height: ha = 20.39660780544
Height: hb = 16.51111108059
Height: hc = 11.55877775641

Median: ma = 24.45991496173
Median: mb = 22.00656810847
Median: mc = 11.83221595662

Inradius: r = 5.09990195136
Circumradius: R = 15.44441456421

Vertex coordinates: A[30; 0] B[0; 0] C[12.46766666667; 11.55877775641]
Centroid: CG[14.15655555556; 3.85325925214]
Coordinates of the circumscribed circle: U[15; -3.67771775338]
Coordinates of the inscribed circle: I[13; 5.09990195136]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.6087575064° = 146°36'27″ = 0.58328077604 rad
∠ B' = β' = 137.1676571934° = 137°10' = 0.74875843497 rad
∠ C' = γ' = 76.2265853002° = 76°13'33″ = 1.81112005436 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 = 21 ; ; c = 30 ; ;

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

p = a+b+c = 17+21+30 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-17)(34-21)(34-30) } ; ; T = sqrt{ 30056 } = 173.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 173.37 }{ 17 } = 20.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 173.37 }{ 21 } = 16.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 173.37 }{ 30 } = 11.56 ; ;

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**2-21**2-30**2 }{ 2 * 21 * 30 } ) = 33° 23'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 42° 50' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-17**2-21**2 }{ 2 * 21 * 17 } ) = 103° 46'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 173.37 }{ 34 } = 5.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 33° 23'33" } = 15.44 ; ;




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