15 26 28 triangle

Acute scalene triangle.

Sides: a = 15   b = 26   c = 28

Area: T = 192.7943769349
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 31.98220267884° = 31°58'55″ = 0.55881916689 rad
Angle ∠ B = β = 66.64548997703° = 66°38'42″ = 1.16331729307 rad
Angle ∠ C = γ = 81.37330734413° = 81°22'23″ = 1.4220228054 rad

Height: ha = 25.70658359133
Height: hb = 14.833028995
Height: hc = 13.7710983525

Median: ma = 25.95766947048
Median: mb = 18.3176659084
Median: mc = 15.95330561335

Inradius: r = 5.58882251985
Circumradius: R = 14.16602086479

Vertex coordinates: A[28; 0] B[0; 0] C[5.94664285714; 13.7710983525]
Centroid: CG[11.31554761905; 4.59903278417]
Coordinates of the circumscribed circle: U[14; 2.12440312972]
Coordinates of the inscribed circle: I[8.5; 5.58882251985]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.0187973212° = 148°1'5″ = 0.55881916689 rad
∠ B' = β' = 113.355510023° = 113°21'18″ = 1.16331729307 rad
∠ C' = γ' = 98.62769265587° = 98°37'37″ = 1.4220228054 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 = 26 ; ; c = 28 ; ;

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

p = a+b+c = 15+26+28 = 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 * (34.5-15)(34.5-26)(34.5-28) } ; ; T = sqrt{ 37169.44 } = 192.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 192.79 }{ 15 } = 25.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 192.79 }{ 26 } = 14.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 192.79 }{ 28 } = 13.77 ; ;

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**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 31° 58'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-15**2-28**2 }{ 2 * 15 * 28 } ) = 66° 38'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-15**2-26**2 }{ 2 * 26 * 15 } ) = 81° 22'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 192.79 }{ 34.5 } = 5.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 31° 58'55" } = 14.16 ; ;




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