16.85 7.35 10.08 triangle

Obtuse scalene triangle.

Sides: a = 16.85   b = 7.35   c = 10.08

Area: T = 18.53552353219
Perimeter: p = 34.28
Semiperimeter: s = 17.14

Angle ∠ A = α = 149.9766359297° = 149°58'35″ = 2.61875812699 rad
Angle ∠ B = β = 12.607666351° = 12°36'24″ = 0.22200277859 rad
Angle ∠ C = γ = 17.41769771926° = 17°25'1″ = 0.30439835978 rad

Height: ha = 2.22000279314
Height: hb = 5.04436014481
Height: hc = 3.67876260559

Median: ma = 2.61441585644
Median: mb = 13.38987574106
Median: mc = 11.98221074941

Inradius: r = 1.08114022942
Circumradius: R = 16.83879680419

Vertex coordinates: A[10.08; 0] B[0; 0] C[16.44437698413; 3.67876260559]
Centroid: CG[8.84112566138; 1.2265875352]
Coordinates of the circumscribed circle: U[5.04; 16.06659754693]
Coordinates of the inscribed circle: I[9.79; 1.08114022942]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 30.02436407026° = 30°1'25″ = 2.61875812699 rad
∠ B' = β' = 167.393333649° = 167°23'36″ = 0.22200277859 rad
∠ C' = γ' = 162.5833022807° = 162°34'59″ = 0.30439835978 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 = 16.85 ; ; b = 7.35 ; ; c = 10.08 ; ;

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

p = a+b+c = 16.85+7.35+10.08 = 34.28 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34.28 }{ 2 } = 17.14 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.14 * (17.14-16.85)(17.14-7.35)(17.14-10.08) } ; ; T = sqrt{ 343.55 } = 18.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18.54 }{ 16.85 } = 2.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18.54 }{ 7.35 } = 5.04 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18.54 }{ 10.08 } = 3.68 ; ;

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{ 7.35**2+10.08**2-16.85**2 }{ 2 * 7.35 * 10.08 } ) = 149° 58'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 16.85**2+10.08**2-7.35**2 }{ 2 * 16.85 * 10.08 } ) = 12° 36'24" ; ;
 gamma = 180° - alpha - beta = 180° - 149° 58'35" - 12° 36'24" = 17° 25'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18.54 }{ 17.14 } = 1.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 16.85 }{ 2 * sin 149° 58'35" } = 16.84 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.35**2+2 * 10.08**2 - 16.85**2 } }{ 2 } = 2.614 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.08**2+2 * 16.85**2 - 7.35**2 } }{ 2 } = 13.389 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.35**2+2 * 16.85**2 - 10.08**2 } }{ 2 } = 11.982 ; ;
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