26 28 30 triangle

Acute scalene triangle.

Sides: a = 26   b = 28   c = 30

Area: T = 336
Perimeter: p = 84
Semiperimeter: s = 42

Angle ∠ A = α = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ B = β = 59.49897625939° = 59°29'23″ = 1.03882922285 rad
Angle ∠ C = γ = 67.3880135052° = 67°22'49″ = 1.17660052071 rad

Height: ha = 25.84661538462
Height: hb = 24
Height: hc = 22.4

Median: ma = 25.94222435421
Median: mb = 24.33110501212
Median: mc = 22.47222050542

Inradius: r = 8
Circumradius: R = 16.25

Vertex coordinates: A[30; 0] B[0; 0] C[13.2; 22.4]
Centroid: CG[14.4; 7.46766666667]
Coordinates of the circumscribed circle: U[15; 6.25]
Coordinates of the inscribed circle: I[14; 8]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ B' = β' = 120.5110237406° = 120°30'37″ = 1.03882922285 rad
∠ C' = γ' = 112.6219864948° = 112°37'11″ = 1.17660052071 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 = 28 ; ; c = 30 ; ;

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

p = a+b+c = 26+28+30 = 84 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 84 }{ 2 } = 42 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 42 * (42-26)(42-28)(42-30) } ; ; T = sqrt{ 112896 } = 336 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 336 }{ 26 } = 25.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 336 }{ 28 } = 24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 336 }{ 30 } = 22.4 ; ;

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**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 53° 7'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 59° 29'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-26**2-28**2 }{ 2 * 28 * 26 } ) = 67° 22'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 336 }{ 42 } = 8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 26 }{ 2 * sin 53° 7'48" } = 16.25 ; ;




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