15 21 28 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 21   c = 28

Area: T = 154.7132636847
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 31.75113162564° = 31°45'5″ = 0.55441650105 rad
Angle ∠ B = β = 47.4533334116° = 47°27'12″ = 0.82882169214 rad
Angle ∠ C = γ = 100.7955349628° = 100°47'43″ = 1.75992107217 rad

Height: ha = 20.62883515795
Height: hb = 14.73545368425
Height: hc = 11.05109026319

Median: ma = 23.58549528301
Median: mb = 19.85657296517
Median: mc = 11.70546999107

Inradius: r = 4.83547699015
Circumradius: R = 14.25222294555

Vertex coordinates: A[28; 0] B[0; 0] C[10.14328571429; 11.05109026319]
Centroid: CG[12.71442857143; 3.68436342106]
Coordinates of the circumscribed circle: U[14; -2.66994651996]
Coordinates of the inscribed circle: I[11; 4.83547699015]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.2498683744° = 148°14'55″ = 0.55441650105 rad
∠ B' = β' = 132.5476665884° = 132°32'48″ = 0.82882169214 rad
∠ C' = γ' = 79.20546503724° = 79°12'17″ = 1.75992107217 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 = 21 ; ; c = 28 ; ;

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

p = a+b+c = 15+21+28 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-15)(32-21)(32-28) } ; ; T = sqrt{ 23936 } = 154.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 154.71 }{ 15 } = 20.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 154.71 }{ 21 } = 14.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 154.71 }{ 28 } = 11.05 ; ;

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**2-21**2-28**2 }{ 2 * 21 * 28 } ) = 31° 45'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-15**2-28**2 }{ 2 * 15 * 28 } ) = 47° 27'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-15**2-21**2 }{ 2 * 21 * 15 } ) = 100° 47'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 154.71 }{ 32 } = 4.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 31° 45'5" } = 14.25 ; ;




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