5 28 30 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 28   c = 30

Area: T = 66.21999811178
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 9.0698721546° = 9°4'7″ = 0.15882790499 rad
Angle ∠ B = β = 61.96657034651° = 61°57'57″ = 1.08215055488 rad
Angle ∠ C = γ = 108.9665574989° = 108°57'56″ = 1.90218080549 rad

Height: ha = 26.48799924471
Height: hb = 4.72985700798
Height: hc = 4.41333320745

Median: ma = 28.90993410509
Median: mb = 16.32548277173
Median: mc = 13.3987761007

Inradius: r = 2.10215867022
Circumradius: R = 15.86110317144

Vertex coordinates: A[30; 0] B[0; 0] C[2.35; 4.41333320745]
Centroid: CG[10.78333333333; 1.47111106915]
Coordinates of the circumscribed circle: U[15; -5.15548353072]
Coordinates of the inscribed circle: I[3.5; 2.10215867022]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.9311278454° = 170°55'53″ = 0.15882790499 rad
∠ B' = β' = 118.0344296535° = 118°2'3″ = 1.08215055488 rad
∠ C' = γ' = 71.03444250112° = 71°2'4″ = 1.90218080549 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 = 5 ; ; b = 28 ; ; c = 30 ; ;

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

p = a+b+c = 5+28+30 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-5)(31.5-28)(31.5-30) } ; ; T = sqrt{ 4382.44 } = 66.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 66.2 }{ 5 } = 26.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 66.2 }{ 28 } = 4.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 66.2 }{ 30 } = 4.41 ; ;

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{ 5**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 9° 4'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-5**2-30**2 }{ 2 * 5 * 30 } ) = 61° 57'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-5**2-28**2 }{ 2 * 28 * 5 } ) = 108° 57'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 66.2 }{ 31.5 } = 2.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 9° 4'7" } = 15.86 ; ;




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