17 24 30 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 24   c = 30

Area: T = 203.8122260426
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 34.48218516526° = 34°28'55″ = 0.60218218435 rad
Angle ∠ B = β = 53.06598546227° = 53°3'35″ = 0.92660691638 rad
Angle ∠ C = γ = 92.45882937248° = 92°27'30″ = 1.61437016463 rad

Height: ha = 23.97879129913
Height: hb = 16.98443550355
Height: hc = 13.58774840284

Median: ma = 25.80221316949
Median: mb = 21.22549852768
Median: mc = 14.40548602909

Inradius: r = 5.74111904345
Circumradius: R = 15.01438170962

Vertex coordinates: A[30; 0] B[0; 0] C[10.21766666667; 13.58774840284]
Centroid: CG[13.40655555556; 4.52991613428]
Coordinates of the circumscribed circle: U[15; -0.6443974998]
Coordinates of the inscribed circle: I[11.5; 5.74111904345]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.5188148347° = 145°31'5″ = 0.60218218435 rad
∠ B' = β' = 126.9440145377° = 126°56'25″ = 0.92660691638 rad
∠ C' = γ' = 87.54217062752° = 87°32'30″ = 1.61437016463 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 = 24 ; ; c = 30 ; ;

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

p = a+b+c = 17+24+30 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-17)(35.5-24)(35.5-30) } ; ; T = sqrt{ 41539.44 } = 203.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 203.81 }{ 17 } = 23.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 203.81 }{ 24 } = 16.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 203.81 }{ 30 } = 13.59 ; ;

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**2-24**2-30**2 }{ 2 * 24 * 30 } ) = 34° 28'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 53° 3'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-17**2-24**2 }{ 2 * 24 * 17 } ) = 92° 27'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 203.81 }{ 35.5 } = 5.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 34° 28'55" } = 15.01 ; ;




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