9 28 30 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 28   c = 30

Area: T = 125.6965813375
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 17.41441079606° = 17°24'51″ = 0.30439335202 rad
Angle ∠ B = β = 68.60438134618° = 68°36'14″ = 1.19773624243 rad
Angle ∠ C = γ = 93.98220785776° = 93°58'55″ = 1.6440296709 rad

Height: ha = 27.93224029722
Height: hb = 8.97882723839
Height: hc = 8.38797208917

Median: ma = 28.66661821664
Median: mb = 17.16110023017
Median: mc = 14.40548602909

Inradius: r = 3.75221138321
Circumradius: R = 15.0366300329

Vertex coordinates: A[30; 0] B[0; 0] C[3.28333333333; 8.38797208917]
Centroid: CG[11.09444444444; 2.79332402972]
Coordinates of the circumscribed circle: U[15; -1.04441875228]
Coordinates of the inscribed circle: I[5.5; 3.75221138321]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.5865892039° = 162°35'9″ = 0.30439335202 rad
∠ B' = β' = 111.3966186538° = 111°23'46″ = 1.19773624243 rad
∠ C' = γ' = 86.01879214224° = 86°1'5″ = 1.6440296709 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 = 9 ; ; b = 28 ; ; c = 30 ; ;

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

p = a+b+c = 9+28+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 * (33.5-9)(33.5-28)(33.5-30) } ; ; T = sqrt{ 15799.44 } = 125.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 125.7 }{ 9 } = 27.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 125.7 }{ 28 } = 8.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 125.7 }{ 30 } = 8.38 ; ;

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{ 9**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 17° 24'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-9**2-30**2 }{ 2 * 9 * 30 } ) = 68° 36'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-9**2-28**2 }{ 2 * 28 * 9 } ) = 93° 58'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 125.7 }{ 33.5 } = 3.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 17° 24'51" } = 15.04 ; ;




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