12 12 22 triangle

Obtuse isosceles triangle.

Sides: a = 12   b = 12   c = 22

Area: T = 52.75441467564
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 23.55664643091° = 23°33'23″ = 0.41111378623 rad
Angle ∠ B = β = 23.55664643091° = 23°33'23″ = 0.41111378623 rad
Angle ∠ C = γ = 132.8877071382° = 132°53'13″ = 2.31993169289 rad

Height: ha = 8.79223577927
Height: hb = 8.79223577927
Height: hc = 4.79658315233

Median: ma = 16.67333320005
Median: mb = 16.67333320005
Median: mc = 4.79658315233

Inradius: r = 2.29436585546
Circumradius: R = 15.01330378121

Vertex coordinates: A[22; 0] B[0; 0] C[11; 4.79658315233]
Centroid: CG[11; 1.59986105078]
Coordinates of the circumscribed circle: U[11; -10.21772062888]
Coordinates of the inscribed circle: I[11; 2.29436585546]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.4443535691° = 156°26'37″ = 0.41111378623 rad
∠ B' = β' = 156.4443535691° = 156°26'37″ = 0.41111378623 rad
∠ C' = γ' = 47.11329286182° = 47°6'47″ = 2.31993169289 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 = 12 ; ; b = 12 ; ; c = 22 ; ;

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

p = a+b+c = 12+12+22 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-12)(23-12)(23-22) } ; ; T = sqrt{ 2783 } = 52.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 52.75 }{ 12 } = 8.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 52.75 }{ 12 } = 8.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 52.75 }{ 22 } = 4.8 ; ;

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{ 12**2-12**2-22**2 }{ 2 * 12 * 22 } ) = 23° 33'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-12**2-22**2 }{ 2 * 12 * 22 } ) = 23° 33'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-12**2-12**2 }{ 2 * 12 * 12 } ) = 132° 53'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 52.75 }{ 23 } = 2.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 23° 33'23" } = 15.01 ; ;




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