12 23 28 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 23   c = 28

Area: T = 135.1811128491
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 24.82330451588° = 24°49'23″ = 0.43332438684 rad
Angle ∠ B = β = 53.57664263577° = 53°34'35″ = 0.93550850414 rad
Angle ∠ C = γ = 101.6010528484° = 101°36'2″ = 1.77332637438 rad

Height: ha = 22.53301880818
Height: hb = 11.75548807383
Height: hc = 9.65657948922

Median: ma = 24.91098374142
Median: mb = 18.21440056001
Median: mc = 11.85332695911

Inradius: r = 4.29114643965
Circumradius: R = 14.29219357278

Vertex coordinates: A[28; 0] B[0; 0] C[7.125; 9.65657948922]
Centroid: CG[11.70883333333; 3.21985982974]
Coordinates of the circumscribed circle: U[14; -2.87439218583]
Coordinates of the inscribed circle: I[8.5; 4.29114643965]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.1776954841° = 155°10'37″ = 0.43332438684 rad
∠ B' = β' = 126.4243573642° = 126°25'25″ = 0.93550850414 rad
∠ C' = γ' = 78.39994715165° = 78°23'58″ = 1.77332637438 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 = 12 ; ; b = 23 ; ; c = 28 ; ;

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

p = a+b+c = 12+23+28 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-12)(31.5-23)(31.5-28) } ; ; T = sqrt{ 18273.94 } = 135.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 135.18 }{ 12 } = 22.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 135.18 }{ 23 } = 11.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 135.18 }{ 28 } = 9.66 ; ;

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{ 12**2-23**2-28**2 }{ 2 * 23 * 28 } ) = 24° 49'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-12**2-28**2 }{ 2 * 12 * 28 } ) = 53° 34'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-12**2-23**2 }{ 2 * 23 * 12 } ) = 101° 36'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 135.18 }{ 31.5 } = 4.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 24° 49'23" } = 14.29 ; ;




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