15 25 28 triangle

Acute scalene triangle.

Sides: a = 15   b = 25   c = 28

Area: T = 186.7732588995
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 32.25114533703° = 32°15'5″ = 0.56328940499 rad
Angle ∠ B = β = 62.79771055878° = 62°47'50″ = 1.09660162532 rad
Angle ∠ C = γ = 84.95114410419° = 84°57'5″ = 1.48326823505 rad

Height: ha = 24.9033011866
Height: hb = 14.94218071196
Height: hc = 13.34108992139

Median: ma = 25.46107541129
Median: mb = 18.66114576065
Median: mc = 15.13327459504

Inradius: r = 5.4933311441
Circumradius: R = 14.05545248857

Vertex coordinates: A[28; 0] B[0; 0] C[6.85771428571; 13.34108992139]
Centroid: CG[11.6199047619; 4.44769664046]
Coordinates of the circumscribed circle: U[14; 1.23767981899]
Coordinates of the inscribed circle: I[9; 5.4933311441]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.749854663° = 147°44'55″ = 0.56328940499 rad
∠ B' = β' = 117.2032894412° = 117°12'10″ = 1.09660162532 rad
∠ C' = γ' = 95.04985589581° = 95°2'55″ = 1.48326823505 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 = 25 ; ; c = 28 ; ;

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

p = a+b+c = 15+25+28 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-15)(34-25)(34-28) } ; ; T = sqrt{ 34884 } = 186.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 186.77 }{ 15 } = 24.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 186.77 }{ 25 } = 14.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 186.77 }{ 28 } = 13.34 ; ;

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**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 32° 15'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-15**2-28**2 }{ 2 * 15 * 28 } ) = 62° 47'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-15**2-25**2 }{ 2 * 25 * 15 } ) = 84° 57'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 186.77 }{ 34 } = 5.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 32° 15'5" } = 14.05 ; ;




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