28 28 30 triangle

Acute isosceles triangle.

Sides: a = 28   b = 28   c = 30

Area: T = 354.6487712526
Perimeter: p = 86
Semiperimeter: s = 43

Angle ∠ A = α = 57.60876345142° = 57°36'27″ = 1.00554428966 rad
Angle ∠ B = β = 57.60876345142° = 57°36'27″ = 1.00554428966 rad
Angle ∠ C = γ = 64.78547309717° = 64°47'5″ = 1.13107068605 rad

Height: ha = 25.33219794662
Height: hb = 25.33219794662
Height: hc = 23.64331808351

Median: ma = 25.41765300543
Median: mb = 25.41765300543
Median: mc = 23.64331808351

Inradius: r = 8.24876212215
Circumradius: R = 16.587983343

Vertex coordinates: A[30; 0] B[0; 0] C[15; 23.64331808351]
Centroid: CG[15; 7.88110602784]
Coordinates of the circumscribed circle: U[15; 7.06333474051]
Coordinates of the inscribed circle: I[15; 8.24876212215]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.3922365486° = 122°23'33″ = 1.00554428966 rad
∠ B' = β' = 122.3922365486° = 122°23'33″ = 1.00554428966 rad
∠ C' = γ' = 115.2155269028° = 115°12'55″ = 1.13107068605 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 = 28 ; ; b = 28 ; ; c = 30 ; ;

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

p = a+b+c = 28+28+30 = 86 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 86 }{ 2 } = 43 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 43 * (43-28)(43-28)(43-30) } ; ; T = sqrt{ 125775 } = 354.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 354.65 }{ 28 } = 25.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 354.65 }{ 28 } = 25.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 354.65 }{ 30 } = 23.64 ; ;

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{ 28**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 57° 36'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 57° 36'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 64° 47'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 354.65 }{ 43 } = 8.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 28 }{ 2 * sin 57° 36'27" } = 16.58 ; ;




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