23 23 28 triangle

Acute isosceles triangle.

Sides: a = 23   b = 23   c = 28

Area: T = 255.4766026273
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 52.50547502354° = 52°30'17″ = 0.91663807645 rad
Angle ∠ B = β = 52.50547502354° = 52°30'17″ = 0.91663807645 rad
Angle ∠ C = γ = 74.99904995291° = 74°59'26″ = 1.30988311245 rad

Height: ha = 22.21553066324
Height: hb = 22.21553066324
Height: hc = 18.24882875909

Median: ma = 22.89765062837
Median: mb = 22.89765062837
Median: mc = 18.24882875909

Inradius: r = 6.90547574668
Circumradius: R = 14.49545107141

Vertex coordinates: A[28; 0] B[0; 0] C[14; 18.24882875909]
Centroid: CG[14; 6.08327625303]
Coordinates of the circumscribed circle: U[14; 3.75437768768]
Coordinates of the inscribed circle: I[14; 6.90547574668]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.4955249765° = 127°29'43″ = 0.91663807645 rad
∠ B' = β' = 127.4955249765° = 127°29'43″ = 0.91663807645 rad
∠ C' = γ' = 105.0109500471° = 105°34″ = 1.30988311245 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 = 23 ; ; c = 28 ; ;

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

p = a+b+c = 23+23+28 = 74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74 }{ 2 } = 37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37 * (37-23)(37-23)(37-28) } ; ; T = sqrt{ 65268 } = 255.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 255.48 }{ 23 } = 22.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 255.48 }{ 23 } = 22.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 255.48 }{ 28 } = 18.25 ; ;

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**2-23**2-28**2 }{ 2 * 23 * 28 } ) = 52° 30'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-23**2-28**2 }{ 2 * 23 * 28 } ) = 52° 30'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-23**2-23**2 }{ 2 * 23 * 23 } ) = 74° 59'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 255.48 }{ 37 } = 6.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 23 }{ 2 * sin 52° 30'17" } = 14.49 ; ;




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