17 18 24 triangle

Acute scalene triangle.

Sides: a = 17   b = 18   c = 24

Area: T = 152.7220128012
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 44.99443970337° = 44°59'40″ = 0.78553003732 rad
Angle ∠ B = β = 48.47216771644° = 48°28'18″ = 0.84659903605 rad
Angle ∠ C = γ = 86.53439258019° = 86°32'2″ = 1.51103019199 rad

Height: ha = 17.96770738838
Height: hb = 16.96989031124
Height: hc = 12.72766773343

Median: ma = 19.43657917256
Median: mb = 18.74883332593
Median: mc = 12.7487548784

Inradius: r = 5.17769534919
Circumradius: R = 12.02219909707

Vertex coordinates: A[24; 0] B[0; 0] C[11.27108333333; 12.72766773343]
Centroid: CG[11.75769444444; 4.24222257781]
Coordinates of the circumscribed circle: U[12; 0.72768197155]
Coordinates of the inscribed circle: I[11.5; 5.17769534919]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.0065602966° = 135°20″ = 0.78553003732 rad
∠ B' = β' = 131.5288322836° = 131°31'42″ = 0.84659903605 rad
∠ C' = γ' = 93.46660741981° = 93°27'58″ = 1.51103019199 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 = 18 ; ; c = 24 ; ;

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

p = a+b+c = 17+18+24 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-17)(29.5-18)(29.5-24) } ; ; T = sqrt{ 23323.44 } = 152.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 152.72 }{ 17 } = 17.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 152.72 }{ 18 } = 16.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 152.72 }{ 24 } = 12.73 ; ;

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**2-18**2-24**2 }{ 2 * 18 * 24 } ) = 44° 59'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-17**2-24**2 }{ 2 * 17 * 24 } ) = 48° 28'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-17**2-18**2 }{ 2 * 18 * 17 } ) = 86° 32'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 152.72 }{ 29.5 } = 5.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 44° 59'40" } = 12.02 ; ;




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