25 26 28 triangle

Acute scalene triangle.

Sides: a = 25   b = 26   c = 28

Area: T = 298.1943624177
Perimeter: p = 79
Semiperimeter: s = 39.5

Angle ∠ A = α = 55.00661147587° = 55°22″ = 0.96600378113 rad
Angle ∠ B = β = 58.42878777762° = 58°25'40″ = 1.02197588421 rad
Angle ∠ C = γ = 66.5666007465° = 66°33'58″ = 1.16217960002 rad

Height: ha = 23.85554899342
Height: hb = 22.93879710906
Height: hc = 21.32995445841

Median: ma = 23.9533079134
Median: mb = 23.14108729308
Median: mc = 21.31990056053

Inradius: r = 7.54992056754
Circumradius: R = 15.25985422058

Vertex coordinates: A[28; 0] B[0; 0] C[13.08992857143; 21.32995445841]
Centroid: CG[13.69664285714; 7.10998481947]
Coordinates of the circumscribed circle: U[14; 6.06882048618]
Coordinates of the inscribed circle: I[13.5; 7.54992056754]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.9943885241° = 124°59'38″ = 0.96600378113 rad
∠ B' = β' = 121.5722122224° = 121°34'20″ = 1.02197588421 rad
∠ C' = γ' = 113.4343992535° = 113°26'2″ = 1.16217960002 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 = 26 ; ; c = 28 ; ;

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

p = a+b+c = 25+26+28 = 79 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 79 }{ 2 } = 39.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39.5 * (39.5-25)(39.5-26)(39.5-28) } ; ; T = sqrt{ 88919.44 } = 298.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 298.19 }{ 25 } = 23.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 298.19 }{ 26 } = 22.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 298.19 }{ 28 } = 21.3 ; ;

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**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 55° 22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 58° 25'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-25**2-26**2 }{ 2 * 26 * 25 } ) = 66° 33'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 298.19 }{ 39.5 } = 7.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 25 }{ 2 * sin 55° 22" } = 15.26 ; ;




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