22 22 28 triangle

Acute isosceles triangle.

Sides: a = 22   b = 22   c = 28

Area: T = 237.5887878479
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 50.47988036414° = 50°28'44″ = 0.8811021326 rad
Angle ∠ B = β = 50.47988036414° = 50°28'44″ = 0.8811021326 rad
Angle ∠ C = γ = 79.04223927173° = 79°2'33″ = 1.38795500016 rad

Height: ha = 21.59988980435
Height: hb = 21.59988980435
Height: hc = 16.97105627485

Median: ma = 22.65495033058
Median: mb = 22.65495033058
Median: mc = 16.97105627485

Inradius: r = 6.65996632911
Circumradius: R = 14.26599867539

Vertex coordinates: A[28; 0] B[0; 0] C[14; 16.97105627485]
Centroid: CG[14; 5.65768542495]
Coordinates of the circumscribed circle: U[14; 2.71105759945]
Coordinates of the inscribed circle: I[14; 6.65996632911]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.5211196359° = 129°31'16″ = 0.8811021326 rad
∠ B' = β' = 129.5211196359° = 129°31'16″ = 0.8811021326 rad
∠ C' = γ' = 100.9587607283° = 100°57'27″ = 1.38795500016 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 = 22 ; ; b = 22 ; ; c = 28 ; ;

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

p = a+b+c = 22+22+28 = 72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-22)(36-22)(36-28) } ; ; T = sqrt{ 56448 } = 237.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 237.59 }{ 22 } = 21.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 237.59 }{ 22 } = 21.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 237.59 }{ 28 } = 16.97 ; ;

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{ 22**2-22**2-28**2 }{ 2 * 22 * 28 } ) = 50° 28'44" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-22**2-28**2 }{ 2 * 22 * 28 } ) = 50° 28'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 79° 2'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 237.59 }{ 36 } = 6.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 50° 28'44" } = 14.26 ; ;




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