11 28 30 triangle

Acute scalene triangle.

Sides: a = 11   b = 28   c = 30

Area: T = 153.9954926865
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 21.50994443897° = 21°30'34″ = 0.37554106249 rad
Angle ∠ B = β = 68.95656238625° = 68°57'20″ = 1.20435026742 rad
Angle ∠ C = γ = 89.53549317478° = 89°32'6″ = 1.56326793545 rad

Height: ha = 27.99990776117
Height: hb = 110.9996376332
Height: hc = 10.26663284576

Median: ma = 28.49112267198
Median: mb = 17.7344147851
Median: mc = 15.0833103129

Inradius: r = 4.46436210685
Circumradius: R = 155.0004941529

Vertex coordinates: A[30; 0] B[0; 0] C[3.95; 10.26663284576]
Centroid: CG[11.31766666667; 3.42221094859]
Coordinates of the circumscribed circle: U[15; 0.12217572577]
Coordinates of the inscribed circle: I[6.5; 4.46436210685]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.491055561° = 158°29'26″ = 0.37554106249 rad
∠ B' = β' = 111.0444376137° = 111°2'40″ = 1.20435026742 rad
∠ C' = γ' = 90.46550682522° = 90°27'54″ = 1.56326793545 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 = 11 ; ; b = 28 ; ; c = 30 ; ;

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

p = a+b+c = 11+28+30 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-11)(34.5-28)(34.5-30) } ; ; T = sqrt{ 23714.44 } = 153.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 153.99 }{ 11 } = 28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 153.99 }{ 28 } = 11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 153.99 }{ 30 } = 10.27 ; ;

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{ 11**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 21° 30'34" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-11**2-30**2 }{ 2 * 11 * 30 } ) = 68° 57'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-11**2-28**2 }{ 2 * 28 * 11 } ) = 89° 32'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 153.99 }{ 34.5 } = 4.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 21° 30'34" } = 15 ; ;




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