3 27 28 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 27   c = 28

Area: T = 38.83329756779
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 5.89765556554° = 5°53'48″ = 0.10329143107 rad
Angle ∠ B = β = 67.60773121946° = 67°36'26″ = 1.18799701962 rad
Angle ∠ C = γ = 106.496613215° = 106°29'46″ = 1.85987081467 rad

Height: ha = 25.88986504519
Height: hb = 2.87765167169
Height: hc = 2.7743783977

Median: ma = 27.46436122897
Median: mb = 14.63772811683
Median: mc = 13.1532946438

Inradius: r = 1.33990681268
Circumradius: R = 14.60109928444

Vertex coordinates: A[28; 0] B[0; 0] C[1.14328571429; 2.7743783977]
Centroid: CG[9.71442857143; 0.9254594659]
Coordinates of the circumscribed circle: U[14; -4.14659609311]
Coordinates of the inscribed circle: I[2; 1.33990681268]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.1033444345° = 174°6'12″ = 0.10329143107 rad
∠ B' = β' = 112.3932687805° = 112°23'34″ = 1.18799701962 rad
∠ C' = γ' = 73.504386785° = 73°30'14″ = 1.85987081467 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 = 3 ; ; b = 27 ; ; c = 28 ; ;

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

p = a+b+c = 3+27+28 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-3)(29-27)(29-28) } ; ; T = sqrt{ 1508 } = 38.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 38.83 }{ 3 } = 25.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 38.83 }{ 27 } = 2.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 38.83 }{ 28 } = 2.77 ; ;

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{ 3**2-27**2-28**2 }{ 2 * 27 * 28 } ) = 5° 53'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-3**2-28**2 }{ 2 * 3 * 28 } ) = 67° 36'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-3**2-27**2 }{ 2 * 27 * 3 } ) = 106° 29'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 38.83 }{ 29 } = 1.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 5° 53'48" } = 14.6 ; ;




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