6 17 20 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 17   c = 20

Area: T = 47.42882352613
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 16.2199911287° = 16°12' = 0.28327417905 rad
Angle ∠ B = β = 52.23295104114° = 52°13'46″ = 0.91215769234 rad
Angle ∠ C = γ = 111.5710578302° = 111°34'14″ = 1.94772739397 rad

Height: ha = 15.80994117538
Height: hb = 5.58797923837
Height: hc = 4.74328235261

Median: ma = 18.3176659084
Median: mb = 12.07326964676
Median: mc = 7.90656941504

Inradius: r = 2.20659644308
Circumradius: R = 10.75330882646

Vertex coordinates: A[20; 0] B[0; 0] C[3.675; 4.74328235261]
Centroid: CG[7.89216666667; 1.58109411754]
Coordinates of the circumscribed circle: U[10; -3.95333412738]
Coordinates of the inscribed circle: I[4.5; 2.20659644308]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.8800088713° = 163°48' = 0.28327417905 rad
∠ B' = β' = 127.7770489589° = 127°46'14″ = 0.91215769234 rad
∠ C' = γ' = 68.42994216984° = 68°25'46″ = 1.94772739397 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 = 6 ; ; b = 17 ; ; c = 20 ; ;

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

p = a+b+c = 6+17+20 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-6)(21.5-17)(21.5-20) } ; ; T = sqrt{ 2249.44 } = 47.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.43 }{ 6 } = 15.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.43 }{ 17 } = 5.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.43 }{ 20 } = 4.74 ; ;

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{ 6**2-17**2-20**2 }{ 2 * 17 * 20 } ) = 16° 12' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-6**2-20**2 }{ 2 * 6 * 20 } ) = 52° 13'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-6**2-17**2 }{ 2 * 17 * 6 } ) = 111° 34'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.43 }{ 21.5 } = 2.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 16° 12' } = 10.75 ; ;




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