23 28 28 triangle

Acute isosceles triangle.

Sides: a = 23   b = 28   c = 28

Area: T = 293.5888040458
Perimeter: p = 79
Semiperimeter: s = 39.5

Angle ∠ A = α = 48.49994260262° = 48°29'58″ = 0.84664746695 rad
Angle ∠ B = β = 65.75502869869° = 65°45'1″ = 1.14875589921 rad
Angle ∠ C = γ = 65.75502869869° = 65°45'1″ = 1.14875589921 rad

Height: ha = 25.52993948224
Height: hb = 20.97105743184
Height: hc = 20.97105743184

Median: ma = 25.52993948224
Median: mb = 21.45992637339
Median: mc = 21.45992637339

Inradius: r = 7.43326086192
Circumradius: R = 15.35548488997

Vertex coordinates: A[28; 0] B[0; 0] C[9.44664285714; 20.97105743184]
Centroid: CG[12.48221428571; 6.99901914395]
Coordinates of the circumscribed circle: U[14; 6.30664557981]
Coordinates of the inscribed circle: I[11.5; 7.43326086192]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.5010573974° = 131°30'2″ = 0.84664746695 rad
∠ B' = β' = 114.2549713013° = 114°14'59″ = 1.14875589921 rad
∠ C' = γ' = 114.2549713013° = 114°14'59″ = 1.14875589921 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 = 23 ; ; b = 28 ; ; c = 28 ; ;

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

p = a+b+c = 23+28+28 = 79 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 79 }{ 2 } = 39.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39.5 * (39.5-23)(39.5-28)(39.5-28) } ; ; T = sqrt{ 86193.94 } = 293.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 293.59 }{ 23 } = 25.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 293.59 }{ 28 } = 20.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 293.59 }{ 28 } = 20.97 ; ;

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{ 23**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 48° 29'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-23**2-28**2 }{ 2 * 23 * 28 } ) = 65° 45'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-23**2-28**2 }{ 2 * 28 * 23 } ) = 65° 45'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 293.59 }{ 39.5 } = 7.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 23 }{ 2 * sin 48° 29'58" } = 15.35 ; ;




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