17 22 23 triangle

Acute scalene triangle.

Sides: a = 17   b = 22   c = 23

Area: T = 176.7711038352
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 44.32327781336° = 44°19'22″ = 0.77435784121 rad
Angle ∠ B = β = 64.71657088213° = 64°42'57″ = 1.13295021967 rad
Angle ∠ C = γ = 70.96215130451° = 70°57'41″ = 1.23985120448 rad

Height: ha = 20.79765927473
Height: hb = 16.07700943956
Height: hc = 15.37113946393

Median: ma = 20.83986659842
Median: mb = 16.97105627485
Median: mc = 15.94552187191

Inradius: r = 5.70222915597
Circumradius: R = 12.16554543643

Vertex coordinates: A[23; 0] B[0; 0] C[7.26108695652; 15.37113946393]
Centroid: CG[10.08769565217; 5.12437982131]
Coordinates of the circumscribed circle: U[11.5; 3.96884102472]
Coordinates of the inscribed circle: I[9; 5.70222915597]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.6777221866° = 135°40'38″ = 0.77435784121 rad
∠ B' = β' = 115.2844291179° = 115°17'3″ = 1.13295021967 rad
∠ C' = γ' = 109.0388486955° = 109°2'19″ = 1.23985120448 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 = 22 ; ; c = 23 ; ;

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

p = a+b+c = 17+22+23 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-17)(31-22)(31-23) } ; ; T = sqrt{ 31248 } = 176.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 176.77 }{ 17 } = 20.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 176.77 }{ 22 } = 16.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 176.77 }{ 23 } = 15.37 ; ;

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**2-22**2-23**2 }{ 2 * 22 * 23 } ) = 44° 19'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-17**2-23**2 }{ 2 * 17 * 23 } ) = 64° 42'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-17**2-22**2 }{ 2 * 22 * 17 } ) = 70° 57'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 176.77 }{ 31 } = 5.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 44° 19'22" } = 12.17 ; ;




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