14 25 28 triangle

Acute scalene triangle.

Sides: a = 14   b = 25   c = 28

Area: T = 174.7555364724
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 29.95437680794° = 29°57'14″ = 0.52327918764 rad
Angle ∠ B = β = 63.07661351049° = 63°4'34″ = 1.1010886237 rad
Angle ∠ C = γ = 86.97700968156° = 86°58'12″ = 1.51879145402 rad

Height: ha = 24.96550521035
Height: hb = 13.9880429178
Height: hc = 12.48325260518

Median: ma = 25.6032734229
Median: mb = 18.26988259064
Median: mc = 14.64658185159

Inradius: r = 5.21765780515
Circumradius: R = 14.02195982187

Vertex coordinates: A[28; 0] B[0; 0] C[6.33992857143; 12.48325260518]
Centroid: CG[11.44664285714; 4.16108420173]
Coordinates of the circumscribed circle: U[14; 0.74110359058]
Coordinates of the inscribed circle: I[8.5; 5.21765780515]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0466231921° = 150°2'46″ = 0.52327918764 rad
∠ B' = β' = 116.9243864895° = 116°55'26″ = 1.1010886237 rad
∠ C' = γ' = 93.03299031844° = 93°1'48″ = 1.51879145402 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 = 14 ; ; b = 25 ; ; c = 28 ; ;

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

p = a+b+c = 14+25+28 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-14)(33.5-25)(33.5-28) } ; ; T = sqrt{ 30539.44 } = 174.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 174.76 }{ 14 } = 24.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 174.76 }{ 25 } = 13.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 174.76 }{ 28 } = 12.48 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 25**2+28**2-14**2 }{ 2 * 25 * 28 } ) = 29° 57'14" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14**2+28**2-25**2 }{ 2 * 14 * 28 } ) = 63° 4'34" ; ; gamma = 180° - alpha - beta = 180° - 29° 57'14" - 63° 4'34" = 86° 58'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 174.76 }{ 33.5 } = 5.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14 }{ 2 * sin 29° 57'14" } = 14.02 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 28**2 - 14**2 } }{ 2 } = 25.603 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 14**2 - 25**2 } }{ 2 } = 18.269 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 14**2 - 28**2 } }{ 2 } = 14.646 ; ;
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