17 27 30 triangle

Acute scalene triangle.

Sides: a = 17   b = 27   c = 30

Area: T = 227.5966133535
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 34.1921852575° = 34°11'31″ = 0.59767604048 rad
Angle ∠ B = β = 63.1933397692° = 63°11'36″ = 1.10329328552 rad
Angle ∠ C = γ = 82.61547497331° = 82°36'53″ = 1.44218993936 rad

Height: ha = 26.776601571
Height: hb = 16.85989728544
Height: hc = 15.1733075569

Median: ma = 27.24442654517
Median: mb = 20.30439405042
Median: mc = 16.85222995464

Inradius: r = 6.15112468523
Circumradius: R = 15.1255476635

Vertex coordinates: A[30; 0] B[0; 0] C[7.66766666667; 15.1733075569]
Centroid: CG[12.55655555556; 5.05876918563]
Coordinates of the circumscribed circle: U[15; 1.94442333801]
Coordinates of the inscribed circle: I[10; 6.15112468523]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.8088147425° = 145°48'29″ = 0.59767604048 rad
∠ B' = β' = 116.8076602308° = 116°48'24″ = 1.10329328552 rad
∠ C' = γ' = 97.38552502669° = 97°23'7″ = 1.44218993936 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 = 30 ; ;

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

p = a+b+c = 17+27+30 = 74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74 }{ 2 } = 37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37 * (37-17)(37-27)(37-30) } ; ; T = sqrt{ 51800 } = 227.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 227.6 }{ 17 } = 26.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 227.6 }{ 27 } = 16.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 227.6 }{ 30 } = 15.17 ; ;

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**2-30**2 }{ 2 * 27 * 30 } ) = 34° 11'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 63° 11'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-17**2-27**2 }{ 2 * 27 * 17 } ) = 82° 36'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 227.6 }{ 37 } = 6.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 34° 11'31" } = 15.13 ; ;




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