17 20 30 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 20   c = 30

Area: T = 161.6098902911
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 32.59549372923° = 32°35'42″ = 0.56988889752 rad
Angle ∠ B = β = 39.32881064337° = 39°19'41″ = 0.68664049458 rad
Angle ∠ C = γ = 108.0776956274° = 108°4'37″ = 1.88662987325 rad

Height: ha = 19.01328121071
Height: hb = 16.16108902911
Height: hc = 10.77439268607

Median: ma = 24.03664306834
Median: mb = 22.23773559579
Median: mc = 10.93216055545

Inradius: r = 4.82441463555
Circumradius: R = 15.77988336785

Vertex coordinates: A[30; 0] B[0; 0] C[13.15; 10.77439268607]
Centroid: CG[14.38333333333; 3.59113089536]
Coordinates of the circumscribed circle: U[15; -4.89660792738]
Coordinates of the inscribed circle: I[13.5; 4.82441463555]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.4055062708° = 147°24'18″ = 0.56988889752 rad
∠ B' = β' = 140.6721893566° = 140°40'19″ = 0.68664049458 rad
∠ C' = γ' = 71.9233043726° = 71°55'23″ = 1.88662987325 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 = 20 ; ; c = 30 ; ;

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

p = a+b+c = 17+20+30 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-17)(33.5-20)(33.5-30) } ; ; T = sqrt{ 26117.44 } = 161.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 161.61 }{ 17 } = 19.01 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 161.61 }{ 20 } = 16.16 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 161.61 }{ 30 } = 10.77 ; ;

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{ 17**2-20**2-30**2 }{ 2 * 20 * 30 } ) = 32° 35'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 39° 19'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-17**2-20**2 }{ 2 * 20 * 17 } ) = 108° 4'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 161.61 }{ 33.5 } = 4.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 32° 35'42" } = 15.78 ; ;




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