16 20 28 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 20   c = 28

Area: T = 156.7677343538
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 34.048773237° = 34°2'52″ = 0.59442450327 rad
Angle ∠ B = β = 44.41553085972° = 44°24'55″ = 0.77551933733 rad
Angle ∠ C = γ = 101.5376959033° = 101°32'13″ = 1.77221542476 rad

Height: ha = 19.59659179423
Height: hb = 15.67767343538
Height: hc = 11.19876673956

Median: ma = 22.97882505862
Median: mb = 20.49439015319
Median: mc = 11.48991252931

Inradius: r = 4.89989794856
Circumradius: R = 14.28986901662

Vertex coordinates: A[28; 0] B[0; 0] C[11.42985714286; 11.19876673956]
Centroid: CG[13.14328571429; 3.73325557985]
Coordinates of the circumscribed circle: U[14; -2.85877380332]
Coordinates of the inscribed circle: I[12; 4.89989794856]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.952226763° = 145°57'8″ = 0.59442450327 rad
∠ B' = β' = 135.5854691403° = 135°35'5″ = 0.77551933733 rad
∠ C' = γ' = 78.46330409672° = 78°27'47″ = 1.77221542476 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 = 16 ; ; b = 20 ; ; c = 28 ; ;

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

p = a+b+c = 16+20+28 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-16)(32-20)(32-28) } ; ; T = sqrt{ 24576 } = 156.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 156.77 }{ 16 } = 19.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 156.77 }{ 20 } = 15.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 156.77 }{ 28 } = 11.2 ; ;

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{ 20**2+28**2-16**2 }{ 2 * 20 * 28 } ) = 34° 2'52" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 16**2+28**2-20**2 }{ 2 * 16 * 28 } ) = 44° 24'55" ; ; gamma = 180° - alpha - beta = 180° - 34° 2'52" - 44° 24'55" = 101° 32'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 156.77 }{ 32 } = 4.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 16 }{ 2 * sin 34° 2'52" } = 14.29 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 28**2 - 16**2 } }{ 2 } = 22.978 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 16**2 - 20**2 } }{ 2 } = 20.494 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 16**2 - 28**2 } }{ 2 } = 11.489 ; ;
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