25 25 28 triangle

Acute isosceles triangle.

Sides: a = 25   b = 25   c = 28

Area: T = 289.9722412481
Perimeter: p = 78
Semiperimeter: s = 39

Angle ∠ A = α = 55.94442022574° = 55°56'39″ = 0.97664105268 rad
Angle ∠ B = β = 55.94442022574° = 55°56'39″ = 0.97664105268 rad
Angle ∠ C = γ = 68.11215954851° = 68°6'42″ = 1.18987716 rad

Height: ha = 23.19877929985
Height: hb = 23.19877929985
Height: hc = 20.71223151772

Median: ma = 23.41547389479
Median: mb = 23.41547389479
Median: mc = 20.71223151772

Inradius: r = 7.43551900636
Circumradius: R = 15.08876421745

Vertex coordinates: A[28; 0] B[0; 0] C[14; 20.71223151772]
Centroid: CG[14; 6.90441050591]
Coordinates of the circumscribed circle: U[14; 5.62546730027]
Coordinates of the inscribed circle: I[14; 7.43551900636]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.0565797743° = 124°3'21″ = 0.97664105268 rad
∠ B' = β' = 124.0565797743° = 124°3'21″ = 0.97664105268 rad
∠ C' = γ' = 111.8888404515° = 111°53'18″ = 1.18987716 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 = 25 ; ; b = 25 ; ; c = 28 ; ;

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

p = a+b+c = 25+25+28 = 78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 78 }{ 2 } = 39 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39 * (39-25)(39-25)(39-28) } ; ; T = sqrt{ 84084 } = 289.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 289.97 }{ 25 } = 23.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 289.97 }{ 25 } = 23.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 289.97 }{ 28 } = 20.71 ; ;

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{ 25**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 55° 56'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 55° 56'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 68° 6'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 289.97 }{ 39 } = 7.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 25 }{ 2 * sin 55° 56'39" } = 15.09 ; ;




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