17 27 28 triangle

Acute scalene triangle.

Sides: a = 17   b = 27   c = 28

Area: T = 221.9198904107
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 35.95105676196° = 35°57'2″ = 0.62774557729 rad
Angle ∠ B = β = 68.81772083269° = 68°49'2″ = 1.20110868673 rad
Angle ∠ C = γ = 75.23222240535° = 75°13'56″ = 1.31330500133 rad

Height: ha = 26.10881063655
Height: hb = 16.43884373413
Height: hc = 15.85113502933

Median: ma = 26.15881727191
Median: mb = 18.82215302247
Median: mc = 17.6921806013

Inradius: r = 6.1644414003
Circumradius: R = 14.47882618359

Vertex coordinates: A[28; 0] B[0; 0] C[6.14328571429; 15.85113502933]
Centroid: CG[11.3810952381; 5.28437834311]
Coordinates of the circumscribed circle: U[14; 3.69105373307]
Coordinates of the inscribed circle: I[9; 6.1644414003]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.049943238° = 144°2'58″ = 0.62774557729 rad
∠ B' = β' = 111.1832791673° = 111°10'58″ = 1.20110868673 rad
∠ C' = γ' = 104.7687775947° = 104°46'4″ = 1.31330500133 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 = 17 ; ; b = 27 ; ; c = 28 ; ;

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

p = a+b+c = 17+27+28 = 72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-17)(36-27)(36-28) } ; ; T = sqrt{ 49248 } = 221.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 221.92 }{ 17 } = 26.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 221.92 }{ 27 } = 16.44 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 221.92 }{ 28 } = 15.85 ; ;

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{ 17**2-27**2-28**2 }{ 2 * 27 * 28 } ) = 35° 57'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-17**2-28**2 }{ 2 * 17 * 28 } ) = 68° 49'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-17**2-27**2 }{ 2 * 27 * 17 } ) = 75° 13'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 221.92 }{ 36 } = 6.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 35° 57'2" } = 14.48 ; ;




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