15 28 30 triangle

Acute scalene triangle.

Sides: a = 15   b = 28   c = 30

Area: T = 208.2244488233
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 29.72107087751° = 29°43'15″ = 0.51987242242 rad
Angle ∠ B = β = 67.73551251499° = 67°44'6″ = 1.18222009531 rad
Angle ∠ C = γ = 82.5444166075° = 82°32'39″ = 1.44106674763 rad

Height: ha = 27.76332650978
Height: hb = 14.87331777309
Height: hc = 13.88216325489

Median: ma = 28.03112325808
Median: mb = 19.14441897191
Median: mc = 16.71882534973

Inradius: r = 5.70547804995
Circumradius: R = 15.12879036713

Vertex coordinates: A[30; 0] B[0; 0] C[5.68333333333; 13.88216325489]
Centroid: CG[11.89444444444; 4.62772108496]
Coordinates of the circumscribed circle: U[15; 1.96330255954]
Coordinates of the inscribed circle: I[8.5; 5.70547804995]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.2799291225° = 150°16'45″ = 0.51987242242 rad
∠ B' = β' = 112.265487485° = 112°15'54″ = 1.18222009531 rad
∠ C' = γ' = 97.4565833925° = 97°27'21″ = 1.44106674763 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 = 15 ; ; b = 28 ; ; c = 30 ; ;

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

p = a+b+c = 15+28+30 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-15)(36.5-28)(36.5-30) } ; ; T = sqrt{ 43357.44 } = 208.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 208.22 }{ 15 } = 27.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 208.22 }{ 28 } = 14.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 208.22 }{ 30 } = 13.88 ; ;

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{ 15**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 29° 43'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-15**2-30**2 }{ 2 * 15 * 30 } ) = 67° 44'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-15**2-28**2 }{ 2 * 28 * 15 } ) = 82° 32'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 208.22 }{ 36.5 } = 5.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 29° 43'15" } = 15.13 ; ;




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