25 28 28 triangle

Acute isosceles triangle.

Sides: a = 25   b = 28   c = 28

Area: T = 313.1876745409
Perimeter: p = 81
Semiperimeter: s = 40.5

Angle ∠ A = α = 53.03295492685° = 53°1'46″ = 0.92655402356 rad
Angle ∠ B = β = 63.48552253657° = 63°29'7″ = 1.1088026209 rad
Angle ∠ C = γ = 63.48552253657° = 63°29'7″ = 1.1088026209 rad

Height: ha = 25.05549396327
Height: hb = 22.37704818149
Height: hc = 22.37704818149

Median: ma = 25.05549396327
Median: mb = 22.55499445676
Median: mc = 22.55499445676

Inradius: r = 7.73330060595
Circumradius: R = 15.6465617421

Vertex coordinates: A[28; 0] B[0; 0] C[11.16107142857; 22.37704818149]
Centroid: CG[13.05435714286; 7.45768272716]
Coordinates of the circumscribed circle: U[14; 6.98546506344]
Coordinates of the inscribed circle: I[12.5; 7.73330060595]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.9770450731° = 126°58'14″ = 0.92655402356 rad
∠ B' = β' = 116.5154774634° = 116°30'53″ = 1.1088026209 rad
∠ C' = γ' = 116.5154774634° = 116°30'53″ = 1.1088026209 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 = 28 ; ; c = 28 ; ;

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

p = a+b+c = 25+28+28 = 81 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 81 }{ 2 } = 40.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 40.5 * (40.5-25)(40.5-28)(40.5-28) } ; ; T = sqrt{ 98085.94 } = 313.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 313.19 }{ 25 } = 25.05 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 313.19 }{ 28 } = 22.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 313.19 }{ 28 } = 22.37 ; ;

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**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 53° 1'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 63° 29'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-25**2-28**2 }{ 2 * 28 * 25 } ) = 63° 29'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 313.19 }{ 40.5 } = 7.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 25 }{ 2 * sin 53° 1'46" } = 15.65 ; ;




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