10 22 28 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 22   c = 28

Area: T = 97.98795897113
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 18.54989996134° = 18°32'56″ = 0.32437411162 rad
Angle ∠ B = β = 44.41553085972° = 44°24'55″ = 0.77551933733 rad
Angle ∠ C = γ = 117.0365691789° = 117°2'8″ = 2.04326581641 rad

Height: ha = 19.59659179423
Height: hb = 8.90772354283
Height: hc = 6.99985421222

Median: ma = 24.67879253585
Median: mb = 17.91664728672
Median: mc = 9.79879589711

Inradius: r = 3.26659863237
Circumradius: R = 15.71875591829

Vertex coordinates: A[28; 0] B[0; 0] C[7.14328571429; 6.99985421222]
Centroid: CG[11.71442857143; 2.33328473741]
Coordinates of the circumscribed circle: U[14; -7.14443450831]
Coordinates of the inscribed circle: I[8; 3.26659863237]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.4511000387° = 161°27'4″ = 0.32437411162 rad
∠ B' = β' = 135.5854691403° = 135°35'5″ = 0.77551933733 rad
∠ C' = γ' = 62.96443082106° = 62°57'52″ = 2.04326581641 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 = 10 ; ; b = 22 ; ; c = 28 ; ;

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

p = a+b+c = 10+22+28 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-10)(30-22)(30-28) } ; ; T = sqrt{ 9600 } = 97.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 97.98 }{ 10 } = 19.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 97.98 }{ 22 } = 8.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 97.98 }{ 28 } = 7 ; ;

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{ 22**2+28**2-10**2 }{ 2 * 22 * 28 } ) = 18° 32'56" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10**2+28**2-22**2 }{ 2 * 10 * 28 } ) = 44° 24'55" ; ; gamma = 180° - alpha - beta = 180° - 18° 32'56" - 44° 24'55" = 117° 2'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 97.98 }{ 30 } = 3.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10 }{ 2 * sin 18° 32'56" } = 15.72 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 28**2 - 10**2 } }{ 2 } = 24.678 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 10**2 - 22**2 } }{ 2 } = 17.916 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 10**2 - 28**2 } }{ 2 } = 9.798 ; ;
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