15 20 28 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 20   c = 28

Area: T = 144.6377261797
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 31.10218950348° = 31°6'7″ = 0.5432830472 rad
Angle ∠ B = β = 43.53111521674° = 43°31'52″ = 0.76597619325 rad
Angle ∠ C = γ = 105.3676952798° = 105°22'1″ = 1.83990002491 rad

Height: ha = 19.28549682395
Height: hb = 14.46437261797
Height: hc = 10.33112329855

Median: ma = 23.14662739982
Median: mb = 20.11221853611
Median: mc = 10.79435165725

Inradius: r = 4.59216591047
Circumradius: R = 14.51990801728

Vertex coordinates: A[28; 0] B[0; 0] C[10.875; 10.33112329855]
Centroid: CG[12.95883333333; 3.44437443285]
Coordinates of the circumscribed circle: U[14; -3.84875562458]
Coordinates of the inscribed circle: I[11.5; 4.59216591047]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.8988104965° = 148°53'53″ = 0.5432830472 rad
∠ B' = β' = 136.4698847833° = 136°28'8″ = 0.76597619325 rad
∠ C' = γ' = 74.63330472022° = 74°37'59″ = 1.83990002491 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 = 20 ; ; c = 28 ; ;

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

p = a+b+c = 15+20+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 * (31.5-15)(31.5-20)(31.5-28) } ; ; T = sqrt{ 20919.94 } = 144.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 144.64 }{ 15 } = 19.28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 144.64 }{ 20 } = 14.46 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 144.64 }{ 28 } = 10.33 ; ;

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**2-20**2-28**2 }{ 2 * 20 * 28 } ) = 31° 6'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-15**2-28**2 }{ 2 * 15 * 28 } ) = 43° 31'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-15**2-20**2 }{ 2 * 20 * 15 } ) = 105° 22'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 144.64 }{ 31.5 } = 4.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 31° 6'7" } = 14.52 ; ;




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