17 19 30 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 19   c = 30

Area: T = 148.9166083752
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 31.50109414399° = 31°30'3″ = 0.55497951456 rad
Angle ∠ B = β = 35.731129198° = 35°43'53″ = 0.6243628691 rad
Angle ∠ C = γ = 112.768776658° = 112°46'4″ = 1.96881688169 rad

Height: ha = 17.52195392649
Height: hb = 15.6755377237
Height: hc = 9.92877389168

Median: ma = 23.62773147014
Median: mb = 22.45655115729
Median: mc = 10

Inradius: r = 4.51326085985
Circumradius: R = 16.26875510863

Vertex coordinates: A[30; 0] B[0; 0] C[13.8; 9.92877389168]
Centroid: CG[14.6; 3.30992463056]
Coordinates of the circumscribed circle: U[15; -6.29554919064]
Coordinates of the inscribed circle: I[14; 4.51326085985]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.499905856° = 148°29'57″ = 0.55497951456 rad
∠ B' = β' = 144.269870802° = 144°16'7″ = 0.6243628691 rad
∠ C' = γ' = 67.23222334198° = 67°13'56″ = 1.96881688169 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 = 30 ; ;

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

p = a+b+c = 17+19+30 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-17)(33-19)(33-30) } ; ; T = sqrt{ 22176 } = 148.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 148.92 }{ 17 } = 17.52 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 148.92 }{ 19 } = 15.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 148.92 }{ 30 } = 9.93 ; ;

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{ 17**2-19**2-30**2 }{ 2 * 19 * 30 } ) = 31° 30'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 35° 43'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-17**2-19**2 }{ 2 * 19 * 17 } ) = 112° 46'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 148.92 }{ 33 } = 4.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 31° 30'3" } = 16.27 ; ;




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