4 25 28 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 25   c = 28

Area: T = 34.9566222622
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 5.73219679652° = 5°43'55″ = 0.11000417136 rad
Angle ∠ B = β = 38.62548328731° = 38°37'29″ = 0.67441305067 rad
Angle ∠ C = γ = 135.6433199162° = 135°38'36″ = 2.36774204333 rad

Height: ha = 17.4788111311
Height: hb = 2.79664978098
Height: hc = 2.49768730444

Median: ma = 26.46769605357
Median: mb = 15.6122494996
Median: mc = 11.15879568022

Inradius: r = 1.22765341271
Circumradius: R = 20.02550469729

Vertex coordinates: A[28; 0] B[0; 0] C[3.125; 2.49768730444]
Centroid: CG[10.375; 0.83222910148]
Coordinates of the circumscribed circle: U[14; -14.31879085856]
Coordinates of the inscribed circle: I[3.5; 1.22765341271]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.2688032035° = 174°16'5″ = 0.11000417136 rad
∠ B' = β' = 141.3755167127° = 141°22'31″ = 0.67441305067 rad
∠ C' = γ' = 44.35768008383° = 44°21'24″ = 2.36774204333 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 = 4 ; ; b = 25 ; ; c = 28 ; ;

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

p = a+b+c = 4+25+28 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-4)(28.5-25)(28.5-28) } ; ; T = sqrt{ 1221.94 } = 34.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34.96 }{ 4 } = 17.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34.96 }{ 25 } = 2.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34.96 }{ 28 } = 2.5 ; ;

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{ 4**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 5° 43'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-4**2-28**2 }{ 2 * 4 * 28 } ) = 38° 37'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-4**2-25**2 }{ 2 * 25 * 4 } ) = 135° 38'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34.96 }{ 28.5 } = 1.23 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 5° 43'55" } = 20.03 ; ;




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