26 28 28 triangle

Acute isosceles triangle.

Sides: a = 26   b = 28   c = 28

Area: T = 322.3989515959
Perimeter: p = 82
Semiperimeter: s = 41

Angle ∠ A = α = 55.32880089924° = 55°19'41″ = 0.96656559255 rad
Angle ∠ B = β = 62.33659955038° = 62°20'10″ = 1.0887968364 rad
Angle ∠ C = γ = 62.33659955038° = 62°20'10″ = 1.0887968364 rad

Height: ha = 24.79991935353
Height: hb = 23.02878225685
Height: hc = 23.02878225685

Median: ma = 24.79991935353
Median: mb = 23.10884400166
Median: mc = 23.10884400166

Inradius: r = 7.86331589258
Circumradius: R = 15.80769656355

Vertex coordinates: A[28; 0] B[0; 0] C[12.07114285714; 23.02878225685]
Centroid: CG[13.35771428571; 7.67659408562]
Coordinates of the circumscribed circle: U[14; 7.33989483308]
Coordinates of the inscribed circle: I[13; 7.86331589258]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.6721991008° = 124°40'19″ = 0.96656559255 rad
∠ B' = β' = 117.6644004496° = 117°39'50″ = 1.0887968364 rad
∠ C' = γ' = 117.6644004496° = 117°39'50″ = 1.0887968364 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 = 26 ; ; b = 28 ; ; c = 28 ; ;

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

p = a+b+c = 26+28+28 = 82 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 82 }{ 2 } = 41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 41 * (41-26)(41-28)(41-28) } ; ; T = sqrt{ 103935 } = 322.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 322.39 }{ 26 } = 24.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 322.39 }{ 28 } = 23.03 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 322.39 }{ 28 } = 23.03 ; ;

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{ 26**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 55° 19'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 62° 20'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-26**2-28**2 }{ 2 * 28 * 26 } ) = 62° 20'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 322.39 }{ 41 } = 7.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 26 }{ 2 * sin 55° 19'41" } = 15.81 ; ;




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