13 22 28 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 22   c = 28

Area: T = 139.1999272627
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 26.86985861119° = 26°52'7″ = 0.4698945293 rad
Angle ∠ B = β = 49.89219743369° = 49°53'31″ = 0.87107792225 rad
Angle ∠ C = γ = 103.2399439551° = 103°14'22″ = 1.80218681381 rad

Height: ha = 21.41552727119
Height: hb = 12.65444793298
Height: hc = 9.94328051877

Median: ma = 24.32659121103
Median: mb = 18.8554707635
Median: mc = 11.42436596588

Inradius: r = 4.41990245279
Circumradius: R = 14.38222590608

Vertex coordinates: A[28; 0] B[0; 0] C[8.375; 9.94328051877]
Centroid: CG[12.125; 3.31442683959]
Coordinates of the circumscribed circle: U[14; -3.29438390506]
Coordinates of the inscribed circle: I[9.5; 4.41990245279]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.1311413888° = 153°7'53″ = 0.4698945293 rad
∠ B' = β' = 130.1088025663° = 130°6'29″ = 0.87107792225 rad
∠ C' = γ' = 76.76105604487° = 76°45'38″ = 1.80218681381 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 = 13 ; ; b = 22 ; ; c = 28 ; ;

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

p = a+b+c = 13+22+28 = 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 * (31.5-13)(31.5-22)(31.5-28) } ; ; T = sqrt{ 19376.44 } = 139.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 139.2 }{ 13 } = 21.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 139.2 }{ 22 } = 12.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 139.2 }{ 28 } = 9.94 ; ;

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{ 13**2-22**2-28**2 }{ 2 * 22 * 28 } ) = 26° 52'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-13**2-28**2 }{ 2 * 13 * 28 } ) = 49° 53'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-13**2-22**2 }{ 2 * 22 * 13 } ) = 103° 14'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 139.2 }{ 31.5 } = 4.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 26° 52'7" } = 14.38 ; ;




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