17 24 28 triangle

Acute scalene triangle.

Sides: a = 17   b = 24   c = 28

Area: T = 202.9922456756
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 37.16772854613° = 37°10'2″ = 0.64986915053 rad
Angle ∠ B = β = 58.53295450954° = 58°31'46″ = 1.02215332716 rad
Angle ∠ C = γ = 84.30331694433° = 84°18'11″ = 1.47113678767 rad

Height: ha = 23.88114655008
Height: hb = 16.9166038063
Height: hc = 14.49994611969

Median: ma = 24.65325860712
Median: mb = 19.81216127562
Median: mc = 15.37985564992

Inradius: r = 5.88438393263
Circumradius: R = 14.0699488323

Vertex coordinates: A[28; 0] B[0; 0] C[8.875; 14.49994611969]
Centroid: CG[12.29216666667; 4.83331537323]
Coordinates of the circumscribed circle: U[14; 1.39766036203]
Coordinates of the inscribed circle: I[10.5; 5.88438393263]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.8332714539° = 142°49'58″ = 0.64986915053 rad
∠ B' = β' = 121.4770454905° = 121°28'14″ = 1.02215332716 rad
∠ C' = γ' = 95.69768305567° = 95°41'49″ = 1.47113678767 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 = 17 ; ; b = 24 ; ; c = 28 ; ;

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

p = a+b+c = 17+24+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 * (34.5-17)(34.5-24)(34.5-28) } ; ; T = sqrt{ 41205.94 } = 202.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 202.99 }{ 17 } = 23.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 202.99 }{ 24 } = 16.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 202.99 }{ 28 } = 14.5 ; ;

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{ 17**2-24**2-28**2 }{ 2 * 24 * 28 } ) = 37° 10'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-17**2-28**2 }{ 2 * 17 * 28 } ) = 58° 31'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-17**2-24**2 }{ 2 * 24 * 17 } ) = 84° 18'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 202.99 }{ 34.5 } = 5.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 37° 10'2" } = 14.07 ; ;




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