22 22 27 triangle

Acute isosceles triangle.

Sides: a = 22   b = 22   c = 27

Area: T = 234.5087862341
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 52.14770972677° = 52°8'50″ = 0.91101385427 rad
Angle ∠ B = β = 52.14770972677° = 52°8'50″ = 0.91101385427 rad
Angle ∠ C = γ = 75.70658054647° = 75°42'21″ = 1.32113155682 rad

Height: ha = 21.31988965765
Height: hb = 21.31988965765
Height: hc = 17.3710952766

Median: ma = 22.03440645365
Median: mb = 22.03440645365
Median: mc = 17.3710952766

Inradius: r = 6.60658552772
Circumradius: R = 13.93113026326

Vertex coordinates: A[27; 0] B[0; 0] C[13.5; 17.3710952766]
Centroid: CG[13.5; 5.79903175887]
Coordinates of the circumscribed circle: U[13.5; 3.44396501335]
Coordinates of the inscribed circle: I[13.5; 6.60658552772]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.8532902732° = 127°51'10″ = 0.91101385427 rad
∠ B' = β' = 127.8532902732° = 127°51'10″ = 0.91101385427 rad
∠ C' = γ' = 104.2944194535° = 104°17'39″ = 1.32113155682 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 = 27 ; ;

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

p = a+b+c = 22+22+27 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-22)(35.5-22)(35.5-27) } ; ; T = sqrt{ 54993.94 } = 234.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 234.51 }{ 22 } = 21.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 234.51 }{ 22 } = 21.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 234.51 }{ 27 } = 17.37 ; ;

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**2-27**2 }{ 2 * 22 * 27 } ) = 52° 8'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-22**2-27**2 }{ 2 * 22 * 27 } ) = 52° 8'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 75° 42'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 234.51 }{ 35.5 } = 6.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 52° 8'50" } = 13.93 ; ;




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