17 29 30 triangle

Acute scalene triangle.

Sides: a = 17   b = 29   c = 30

Area: T = 239.7699812265
Perimeter: p = 76
Semiperimeter: s = 38

Angle ∠ A = α = 33.43879821579° = 33°26'17″ = 0.58436028839 rad
Angle ∠ B = β = 70.0511432774° = 70°3'5″ = 1.22326281476 rad
Angle ∠ C = γ = 76.51105850682° = 76°30'38″ = 1.33553616221 rad

Height: ha = 28.21999779136
Height: hb = 16.53110215355
Height: hc = 15.98799874844

Median: ma = 28.25333183892
Median: mb = 19.60222957839
Median: mc = 18.43990889146

Inradius: r = 6.30878897965
Circumradius: R = 15.42655439963

Vertex coordinates: A[30; 0] B[0; 0] C[5.8; 15.98799874844]
Centroid: CG[11.93333333333; 5.32766624948]
Coordinates of the circumscribed circle: U[15; 3.59882506279]
Coordinates of the inscribed circle: I[9; 6.30878897965]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.5622017842° = 146°33'43″ = 0.58436028839 rad
∠ B' = β' = 109.9498567226° = 109°56'55″ = 1.22326281476 rad
∠ C' = γ' = 103.4899414932° = 103°29'22″ = 1.33553616221 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 = 29 ; ; c = 30 ; ;

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

p = a+b+c = 17+29+30 = 76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 76 }{ 2 } = 38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38 * (38-17)(38-29)(38-30) } ; ; T = sqrt{ 57456 } = 239.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 239.7 }{ 17 } = 28.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 239.7 }{ 29 } = 16.53 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 239.7 }{ 30 } = 15.98 ; ;

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**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 33° 26'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 70° 3'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-17**2-29**2 }{ 2 * 29 * 17 } ) = 76° 30'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 239.7 }{ 38 } = 6.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 33° 26'17" } = 15.43 ; ;




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