9.2 15.1 17.4 triangle

Acute scalene triangle.

Sides: a = 9.2   b = 15.1   c = 17.4

Area: T = 69.41659804638
Perimeter: p = 41.7
Semiperimeter: s = 20.85

Angle ∠ A = α = 31.89774501112° = 31°53'51″ = 0.55767155274 rad
Angle ∠ B = β = 60.1422482921° = 60°8'33″ = 1.05496843473 rad
Angle ∠ C = γ = 87.96600669679° = 87°57'36″ = 1.53551927789 rad

Height: ha = 15.09904305356
Height: hb = 9.19441695979
Height: hc = 7.97988483292

Median: ma = 15.62876997668
Median: mb = 11.69217706101
Median: mc = 8.98796993268

Inradius: r = 3.32993036194
Circumradius: R = 8.70655170288

Vertex coordinates: A[17.4; 0] B[0; 0] C[4.58801724138; 7.97988483292]
Centroid: CG[7.32767241379; 2.66596161097]
Coordinates of the circumscribed circle: U[8.7; 0.31098818148]
Coordinates of the inscribed circle: I[5.75; 3.32993036194]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.1032549889° = 148°6'9″ = 0.55767155274 rad
∠ B' = β' = 119.8587517079° = 119°51'27″ = 1.05496843473 rad
∠ C' = γ' = 92.04399330321° = 92°2'24″ = 1.53551927789 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 = 9.2 ; ; b = 15.1 ; ; c = 17.4 ; ;

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

p = a+b+c = 9.2+15.1+17.4 = 41.7 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41.7 }{ 2 } = 20.85 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.85 * (20.85-9.2)(20.85-15.1)(20.85-17.4) } ; ; T = sqrt{ 4818.58 } = 69.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 69.42 }{ 9.2 } = 15.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 69.42 }{ 15.1 } = 9.19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 69.42 }{ 17.4 } = 7.98 ; ;

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{ 9.2**2-15.1**2-17.4**2 }{ 2 * 15.1 * 17.4 } ) = 31° 53'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15.1**2-9.2**2-17.4**2 }{ 2 * 9.2 * 17.4 } ) = 60° 8'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17.4**2-9.2**2-15.1**2 }{ 2 * 15.1 * 9.2 } ) = 87° 57'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 69.42 }{ 20.85 } = 3.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9.2 }{ 2 * sin 31° 53'51" } = 8.71 ; ;




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