26 27 28 triangle

Acute scalene triangle.

Sides: a = 26   b = 27   c = 28

Area: T = 314.7999043042
Perimeter: p = 81
Semiperimeter: s = 40.5

Angle ∠ A = α = 56.38876254015° = 56°23'15″ = 0.98441497206 rad
Angle ∠ B = β = 59.86435885334° = 59°51'49″ = 1.0454816722 rad
Angle ∠ C = γ = 63.7498786065° = 63°44'56″ = 1.1132626211 rad

Height: ha = 24.21553110032
Height: hb = 23.31884476327
Height: hc = 22.48656459316

Median: ma = 24.23883992871
Median: mb = 23.40440594769
Median: mc = 22.50655548699

Inradius: r = 7.77328158776
Circumradius: R = 15.61099585072

Vertex coordinates: A[28; 0] B[0; 0] C[13.05435714286; 22.48656459316]
Centroid: CG[13.68545238095; 7.49552153105]
Coordinates of the circumscribed circle: U[14; 6.90444047244]
Coordinates of the inscribed circle: I[13.5; 7.77328158776]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 123.6122374598° = 123°36'45″ = 0.98441497206 rad
∠ B' = β' = 120.1366411467° = 120°8'11″ = 1.0454816722 rad
∠ C' = γ' = 116.2511213935° = 116°15'4″ = 1.1132626211 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 = 26 ; ; b = 27 ; ; c = 28 ; ;

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

p = a+b+c = 26+27+28 = 81 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 81 }{ 2 } = 40.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 40.5 * (40.5-26)(40.5-27)(40.5-28) } ; ; T = sqrt{ 99098.44 } = 314.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 314.8 }{ 26 } = 24.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 314.8 }{ 27 } = 23.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 314.8 }{ 28 } = 22.49 ; ;

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{ 26**2-27**2-28**2 }{ 2 * 27 * 28 } ) = 56° 23'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 59° 51'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-26**2-27**2 }{ 2 * 27 * 26 } ) = 63° 44'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 314.8 }{ 40.5 } = 7.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 26 }{ 2 * sin 56° 23'15" } = 15.61 ; ;




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