22 28 28 triangle

Acute isosceles triangle.

Sides: a = 22   b = 28   c = 28

Area: T = 283.2376650171
Perimeter: p = 78
Semiperimeter: s = 39

Angle ∠ A = α = 46.26547927986° = 46°15'53″ = 0.80774729621 rad
Angle ∠ B = β = 66.86876036007° = 66°52'3″ = 1.16770598458 rad
Angle ∠ C = γ = 66.86876036007° = 66°52'3″ = 1.16770598458 rad

Height: ha = 25.74987863792
Height: hb = 20.23111892979
Height: hc = 20.23111892979

Median: ma = 25.74987863792
Median: mb = 20.92884495365
Median: mc = 20.92884495365

Inradius: r = 7.26224782095
Circumradius: R = 15.22440184927

Vertex coordinates: A[28; 0] B[0; 0] C[8.64328571429; 20.23111892979]
Centroid: CG[12.21442857143; 6.7443729766]
Coordinates of the circumscribed circle: U[14; 5.98108644078]
Coordinates of the inscribed circle: I[11; 7.26224782095]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.7355207201° = 133°44'7″ = 0.80774729621 rad
∠ B' = β' = 113.1322396399° = 113°7'57″ = 1.16770598458 rad
∠ C' = γ' = 113.1322396399° = 113°7'57″ = 1.16770598458 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 = 28 ; ; c = 28 ; ;

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

p = a+b+c = 22+28+28 = 78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 78 }{ 2 } = 39 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39 * (39-22)(39-28)(39-28) } ; ; T = sqrt{ 80223 } = 283.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 283.24 }{ 22 } = 25.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 283.24 }{ 28 } = 20.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 283.24 }{ 28 } = 20.23 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 28**2+28**2-22**2 }{ 2 * 28 * 28 } ) = 46° 15'53" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 22**2+28**2-28**2 }{ 2 * 22 * 28 } ) = 66° 52'3" ; ; gamma = 180° - alpha - beta = 180° - 46° 15'53" - 66° 52'3" = 66° 52'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 283.24 }{ 39 } = 7.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 22 }{ 2 * sin 46° 15'53" } = 15.22 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 28**2 - 22**2 } }{ 2 } = 25.749 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 22**2 - 28**2 } }{ 2 } = 20.928 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 22**2 - 28**2 } }{ 2 } = 20.928 ; ;
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