17.09 19.1 8.54 triangle

Acute scalene triangle.

Sides: a = 17.09   b = 19.1   c = 8.54

Area: T = 72.97442845896
Perimeter: p = 44.73
Semiperimeter: s = 22.365

Angle ∠ A = α = 63.47881592307° = 63°28'41″ = 1.10879028817 rad
Angle ∠ B = β = 89.96327642535° = 89°57'46″ = 1.57701464404 rad
Angle ∠ C = γ = 26.55990765158° = 26°33'33″ = 0.46435433315 rad

Height: ha = 8.54399981966
Height: hb = 7.64112863445
Height: hc = 17.0989996391

Median: ma = 12.07769936242
Median: mb = 9.55549646781
Median: mc = 17.61326701553

Inradius: r = 3.26328788102
Circumradius: R = 9.55500020167

Vertex coordinates: A[8.54; 0] B[0; 0] C[0.01111065574; 17.0989996391]
Centroid: CG[2.85503688525; 5.69766654637]
Coordinates of the circumscribed circle: U[4.27; 8.54222267893]
Coordinates of the inscribed circle: I[3.265; 3.26328788102]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.5221840769° = 116°31'19″ = 1.10879028817 rad
∠ B' = β' = 90.03772357465° = 90°2'14″ = 1.57701464404 rad
∠ C' = γ' = 153.4410923484° = 153°26'27″ = 0.46435433315 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 = 17.09 ; ; b = 19.1 ; ; c = 8.54 ; ;

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

p = a+b+c = 17.09+19.1+8.54 = 44.73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44.73 }{ 2 } = 22.37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.37 * (22.37-17.09)(22.37-19.1)(22.37-8.54) } ; ; T = sqrt{ 5325.25 } = 72.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 72.97 }{ 17.09 } = 8.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 72.97 }{ 19.1 } = 7.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 72.97 }{ 8.54 } = 17.09 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 19.1**2+8.54**2-17.09**2 }{ 2 * 19.1 * 8.54 } ) = 63° 28'41" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 17.09**2+8.54**2-19.1**2 }{ 2 * 17.09 * 8.54 } ) = 89° 57'46" ; ;
 gamma = 180° - alpha - beta = 180° - 63° 28'41" - 89° 57'46" = 26° 33'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 72.97 }{ 22.37 } = 3.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 17.09 }{ 2 * sin 63° 28'41" } = 9.55 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 19.1**2+2 * 8.54**2 - 17.09**2 } }{ 2 } = 12.077 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.54**2+2 * 17.09**2 - 19.1**2 } }{ 2 } = 9.555 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 19.1**2+2 * 17.09**2 - 8.54**2 } }{ 2 } = 17.613 ; ;
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