9 22 22 triangle

Acute isosceles triangle.

Sides: a = 9   b = 22   c = 22

Area: T = 96.90768496031
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 23.60657833806° = 23°36'21″ = 0.41219986425 rad
Angle ∠ B = β = 78.19771083097° = 78°11'50″ = 1.36547970055 rad
Angle ∠ C = γ = 78.19771083097° = 78°11'50″ = 1.36547970055 rad

Height: ha = 21.53548554674
Height: hb = 8.81097136003
Height: hc = 8.81097136003

Median: ma = 21.53548554674
Median: mb = 12.70882650271
Median: mc = 12.70882650271

Inradius: r = 3.65768622492
Circumradius: R = 11.23875957371

Vertex coordinates: A[22; 0] B[0; 0] C[1.84109090909; 8.81097136003]
Centroid: CG[7.9476969697; 2.93765712001]
Coordinates of the circumscribed circle: U[11; 2.29985991281]
Coordinates of the inscribed circle: I[4.5; 3.65768622492]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.3944216619° = 156°23'39″ = 0.41219986425 rad
∠ B' = β' = 101.803289169° = 101°48'10″ = 1.36547970055 rad
∠ C' = γ' = 101.803289169° = 101°48'10″ = 1.36547970055 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 = 9 ; ; b = 22 ; ; c = 22 ; ;

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

p = a+b+c = 9+22+22 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-9)(26.5-22)(26.5-22) } ; ; T = sqrt{ 9390.94 } = 96.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 96.91 }{ 9 } = 21.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 96.91 }{ 22 } = 8.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 96.91 }{ 22 } = 8.81 ; ;

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{ 9**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 23° 36'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-9**2-22**2 }{ 2 * 9 * 22 } ) = 78° 11'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-9**2-22**2 }{ 2 * 22 * 9 } ) = 78° 11'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 96.91 }{ 26.5 } = 3.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 23° 36'21" } = 11.24 ; ;




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