17 18 20 triangle

Acute scalene triangle.

Sides: a = 17   b = 18   c = 20

Area: T = 143.4344436242
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 52.8311100344° = 52°49'52″ = 0.92220766485 rad
Angle ∠ B = β = 57.53663312514° = 57°32'11″ = 1.00441984199 rad
Angle ∠ C = γ = 69.63325684046° = 69°37'57″ = 1.21553175853 rad

Height: ha = 16.87546395579
Height: hb = 15.93771595824
Height: hc = 14.34334436242

Median: ma = 17.02220445305
Median: mb = 16.23326830807
Median: mc = 14.37701078632

Inradius: r = 5.21657976815
Circumradius: R = 10.66768945066

Vertex coordinates: A[20; 0] B[0; 0] C[9.125; 14.34334436242]
Centroid: CG[9.70883333333; 4.78111478747]
Coordinates of the circumscribed circle: U[10; 3.71224975979]
Coordinates of the inscribed circle: I[9.5; 5.21657976815]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.1698899656° = 127°10'8″ = 0.92220766485 rad
∠ B' = β' = 122.4643668749° = 122°27'49″ = 1.00441984199 rad
∠ C' = γ' = 110.3677431595° = 110°22'3″ = 1.21553175853 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 = 17 ; ; b = 18 ; ; c = 20 ; ;

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

p = a+b+c = 17+18+20 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-17)(27.5-18)(27.5-20) } ; ; T = sqrt{ 20573.44 } = 143.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 143.43 }{ 17 } = 16.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 143.43 }{ 18 } = 15.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 143.43 }{ 20 } = 14.34 ; ;

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{ 17**2-18**2-20**2 }{ 2 * 18 * 20 } ) = 52° 49'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-17**2-20**2 }{ 2 * 17 * 20 } ) = 57° 32'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-17**2-18**2 }{ 2 * 18 * 17 } ) = 69° 37'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 143.43 }{ 27.5 } = 5.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 52° 49'52" } = 10.67 ; ;




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