25 27 28 triangle

Acute scalene triangle.

Sides: a = 25   b = 27   c = 28

Area: T = 305.9411170816
Perimeter: p = 80
Semiperimeter: s = 40

Angle ∠ A = α = 54.03442464357° = 54°2'3″ = 0.94330755091 rad
Angle ∠ B = β = 60.9410718932° = 60°56'27″ = 1.06436161939 rad
Angle ∠ C = γ = 65.02550346323° = 65°1'30″ = 1.13549009506 rad

Height: ha = 24.47552936652
Height: hb = 22.66223089493
Height: hc = 21.85329407725

Median: ma = 24.5
Median: mb = 22.85327897641
Median: mc = 21.93217121995

Inradius: r = 7.64985292704
Circumradius: R = 15.44441456421

Vertex coordinates: A[28; 0] B[0; 0] C[12.14328571429; 21.85329407725]
Centroid: CG[13.3810952381; 7.28443135908]
Coordinates of the circumscribed circle: U[14; 6.52108614933]
Coordinates of the inscribed circle: I[13; 7.64985292704]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.9665753564° = 125°57'57″ = 0.94330755091 rad
∠ B' = β' = 119.0599281068° = 119°3'33″ = 1.06436161939 rad
∠ C' = γ' = 114.9754965368° = 114°58'30″ = 1.13549009506 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 = 25 ; ; b = 27 ; ; c = 28 ; ;

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

p = a+b+c = 25+27+28 = 80 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 80 }{ 2 } = 40 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 40 * (40-25)(40-27)(40-28) } ; ; T = sqrt{ 93600 } = 305.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 305.94 }{ 25 } = 24.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 305.94 }{ 27 } = 22.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 305.94 }{ 28 } = 21.85 ; ;

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{ 25**2-27**2-28**2 }{ 2 * 27 * 28 } ) = 54° 2'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 60° 56'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-25**2-27**2 }{ 2 * 27 * 25 } ) = 65° 1'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 305.94 }{ 40 } = 7.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 25 }{ 2 * sin 54° 2'3" } = 15.44 ; ;




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