8 22 22 triangle

Acute isosceles triangle.

Sides: a = 8   b = 22   c = 22

Area: T = 86.53332306111
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 20.95113633928° = 20°57'5″ = 0.3665670274 rad
Angle ∠ B = β = 79.52443183036° = 79°31'28″ = 1.38879611898 rad
Angle ∠ C = γ = 79.52443183036° = 79°31'28″ = 1.38879611898 rad

Height: ha = 21.63333076528
Height: hb = 7.86766573283
Height: hc = 7.86766573283

Median: ma = 21.63333076528
Median: mb = 12.36993168769
Median: mc = 12.36993168769

Inradius: r = 3.32882011774
Circumradius: R = 11.18664539572

Vertex coordinates: A[22; 0] B[0; 0] C[1.45545454545; 7.86766573283]
Centroid: CG[7.81881818182; 2.62222191094]
Coordinates of the circumscribed circle: U[11; 2.03439007195]
Coordinates of the inscribed circle: I[4; 3.32882011774]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.0498636607° = 159°2'55″ = 0.3665670274 rad
∠ B' = β' = 100.4765681696° = 100°28'32″ = 1.38879611898 rad
∠ C' = γ' = 100.4765681696° = 100°28'32″ = 1.38879611898 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 = 8 ; ; b = 22 ; ; c = 22 ; ;

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

p = a+b+c = 8+22+22 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-8)(26-22)(26-22) } ; ; T = sqrt{ 7488 } = 86.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 86.53 }{ 8 } = 21.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 86.53 }{ 22 } = 7.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 86.53 }{ 22 } = 7.87 ; ;

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{ 8**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 20° 57'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-8**2-22**2 }{ 2 * 8 * 22 } ) = 79° 31'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-8**2-22**2 }{ 2 * 22 * 8 } ) = 79° 31'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 86.53 }{ 26 } = 3.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 20° 57'5" } = 11.19 ; ;




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