22 30 30 triangle

Acute isosceles triangle.

Sides: a = 22   b = 30   c = 30

Area: T = 307.0166286213
Perimeter: p = 82
Semiperimeter: s = 41

Angle ∠ A = α = 43.02203765338° = 43°1'13″ = 0.7510847216 rad
Angle ∠ B = β = 68.49898117331° = 68°29'23″ = 1.19553727188 rad
Angle ∠ C = γ = 68.49898117331° = 68°29'23″ = 1.19553727188 rad

Height: ha = 27.91105714739
Height: hb = 20.46877524142
Height: hc = 20.46877524142

Median: ma = 27.91105714739
Median: mb = 21.6110182785
Median: mc = 21.6110182785

Inradius: r = 7.48882021028
Circumradius: R = 16.12329231878

Vertex coordinates: A[30; 0] B[0; 0] C[8.06766666667; 20.46877524142]
Centroid: CG[12.68988888889; 6.82325841381]
Coordinates of the circumscribed circle: U[15; 5.91217385022]
Coordinates of the inscribed circle: I[11; 7.48882021028]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.9879623466° = 136°58'47″ = 0.7510847216 rad
∠ B' = β' = 111.5110188267° = 111°30'37″ = 1.19553727188 rad
∠ C' = γ' = 111.5110188267° = 111°30'37″ = 1.19553727188 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 = 30 ; ; c = 30 ; ;

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

p = a+b+c = 22+30+30 = 82 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 82 }{ 2 } = 41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 41 * (41-22)(41-30)(41-30) } ; ; T = sqrt{ 94259 } = 307.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 307.02 }{ 22 } = 27.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 307.02 }{ 30 } = 20.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 307.02 }{ 30 } = 20.47 ; ;

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**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 43° 1'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-22**2-30**2 }{ 2 * 22 * 30 } ) = 68° 29'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-22**2-30**2 }{ 2 * 30 * 22 } ) = 68° 29'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 307.02 }{ 41 } = 7.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 43° 1'13" } = 16.12 ; ;




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