7 24 27 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 24   c = 27

Area: T = 79.87549021909
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 14.27221207873° = 14°16'20″ = 0.2499095499 rad
Angle ∠ B = β = 57.69773438194° = 57°41'50″ = 1.00770086193 rad
Angle ∠ C = γ = 108.0310535393° = 108°1'50″ = 1.88554885353 rad

Height: ha = 22.8211400626
Height: hb = 6.65662418492
Height: hc = 5.91766594215

Median: ma = 25.30331618578
Median: mb = 15.65224758425
Median: mc = 11.41327122105

Inradius: r = 2.75443069721
Circumradius: R = 14.19772004835

Vertex coordinates: A[27; 0] B[0; 0] C[3.74107407407; 5.91766594215]
Centroid: CG[10.24769135802; 1.97222198072]
Coordinates of the circumscribed circle: U[13.5; -4.39443715782]
Coordinates of the inscribed circle: I[5; 2.75443069721]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.7287879213° = 165°43'40″ = 0.2499095499 rad
∠ B' = β' = 122.3032656181° = 122°18'10″ = 1.00770086193 rad
∠ C' = γ' = 71.96994646067° = 71°58'10″ = 1.88554885353 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 = 7 ; ; b = 24 ; ; c = 27 ; ;

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

p = a+b+c = 7+24+27 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-7)(29-24)(29-27) } ; ; T = sqrt{ 6380 } = 79.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 79.87 }{ 7 } = 22.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 79.87 }{ 24 } = 6.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 79.87 }{ 27 } = 5.92 ; ;

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{ 7**2-24**2-27**2 }{ 2 * 24 * 27 } ) = 14° 16'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-7**2-27**2 }{ 2 * 7 * 27 } ) = 57° 41'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-7**2-24**2 }{ 2 * 24 * 7 } ) = 108° 1'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 79.87 }{ 29 } = 2.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 14° 16'20" } = 14.2 ; ;




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