17 27 29 triangle

Acute scalene triangle.

Sides: a = 17   b = 27   c = 29

Area: T = 225.1943666652
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 35.11441523899° = 35°6'51″ = 0.61328575733 rad
Angle ∠ B = β = 66.00326925267° = 66°10″ = 1.15219642998 rad
Angle ∠ C = γ = 78.88331550833° = 78°52'59″ = 1.37767707806 rad

Height: ha = 26.49333725472
Height: hb = 16.68110123446
Height: hc = 15.53105977001

Median: ma = 26.69773781484
Median: mb = 19.56439975465
Median: mc = 17.28443860174

Inradius: r = 6.17696894973
Circumradius: R = 14.77772805935

Vertex coordinates: A[29; 0] B[0; 0] C[6.91437931034; 15.53105977001]
Centroid: CG[11.97112643678; 5.17768659]
Coordinates of the circumscribed circle: U[14.5; 2.84992142321]
Coordinates of the inscribed circle: I[9.5; 6.17696894973]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.886584761° = 144°53'9″ = 0.61328575733 rad
∠ B' = β' = 113.9977307473° = 113°59'50″ = 1.15219642998 rad
∠ C' = γ' = 101.1176844917° = 101°7'1″ = 1.37767707806 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 = 27 ; ; c = 29 ; ;

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

p = a+b+c = 17+27+29 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-17)(36.5-27)(36.5-29) } ; ; T = sqrt{ 50712.19 } = 225.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 225.19 }{ 17 } = 26.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 225.19 }{ 27 } = 16.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 225.19 }{ 29 } = 15.53 ; ;

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**2-27**2-29**2 }{ 2 * 27 * 29 } ) = 35° 6'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-17**2-29**2 }{ 2 * 17 * 29 } ) = 66° 10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-17**2-27**2 }{ 2 * 27 * 17 } ) = 78° 52'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 225.19 }{ 36.5 } = 6.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 35° 6'51" } = 14.78 ; ;




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