8 17 24 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 17   c = 24

Area: T = 38.93550420573
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 11.00328632015° = 11°10″ = 0.192203619 rad
Angle ∠ B = β = 23.92770614889° = 23°55'37″ = 0.41876060033 rad
Angle ∠ C = γ = 145.077007531° = 145°4'12″ = 2.53219504603 rad

Height: ha = 9.73437605143
Height: hb = 4.58105931832
Height: hc = 3.24545868381

Median: ma = 20.4088331632
Median: mb = 15.74400762387
Median: mc = 5.70108771255

Inradius: r = 1.58991853901
Circumradius: R = 20.9587984296

Vertex coordinates: A[24; 0] B[0; 0] C[7.31325; 3.24545868381]
Centroid: CG[10.43875; 1.0821528946]
Coordinates of the circumscribed circle: U[12; -17.18224650662]
Coordinates of the inscribed circle: I[7.5; 1.58991853901]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.9977136798° = 168°59'50″ = 0.192203619 rad
∠ B' = β' = 156.0732938511° = 156°4'23″ = 0.41876060033 rad
∠ C' = γ' = 34.93299246904° = 34°55'48″ = 2.53219504603 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 = 8 ; ; b = 17 ; ; c = 24 ; ;

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

p = a+b+c = 8+17+24 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-8)(24.5-17)(24.5-24) } ; ; T = sqrt{ 1515.94 } = 38.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 38.94 }{ 8 } = 9.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 38.94 }{ 17 } = 4.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 38.94 }{ 24 } = 3.24 ; ;

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{ 8**2-17**2-24**2 }{ 2 * 17 * 24 } ) = 11° 10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-8**2-24**2 }{ 2 * 8 * 24 } ) = 23° 55'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-8**2-17**2 }{ 2 * 17 * 8 } ) = 145° 4'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 38.94 }{ 24.5 } = 1.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 11° 10" } = 20.96 ; ;




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