15.62 7.81 17.46 triangle

Acute scalene triangle.

Sides: a = 15.62   b = 7.81   c = 17.46

Area: T = 60.99660914876
Perimeter: p = 40.89
Semiperimeter: s = 20.445

Angle ∠ A = α = 63.45991668033° = 63°27'33″ = 1.10875714013 rad
Angle ∠ B = β = 26.57111032727° = 26°34'16″ = 0.4643753238 rad
Angle ∠ C = γ = 89.9769729924° = 89°58'11″ = 1.57702680143 rad

Height: ha = 7.81099989101
Height: hb = 15.62199978201
Height: hc = 6.98769520604

Median: ma = 11.0422089929
Median: mb = 16.09987258813
Median: mc = 8.73436905143

Inradius: r = 2.98334234036
Circumradius: R = 8.73300012183

Vertex coordinates: A[17.46; 0] B[0; 0] C[13.97702147766; 6.98769520604]
Centroid: CG[10.47767382589; 2.32989840201]
Coordinates of the circumscribed circle: U[8.73; 0.00546121685]
Coordinates of the inscribed circle: I[12.635; 2.98334234036]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.5410833197° = 116°32'27″ = 1.10875714013 rad
∠ B' = β' = 153.4298896727° = 153°25'44″ = 0.4643753238 rad
∠ C' = γ' = 90.0330270076° = 90°1'49″ = 1.57702680143 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 = 15.62 ; ; b = 7.81 ; ; c = 17.46 ; ;

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

p = a+b+c = 15.62+7.81+17.46 = 40.89 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40.89 }{ 2 } = 20.45 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.45 * (20.45-15.62)(20.45-7.81)(20.45-17.46) } ; ; T = sqrt{ 3720.52 } = 61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 61 }{ 15.62 } = 7.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 61 }{ 7.81 } = 15.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 61 }{ 17.46 } = 6.99 ; ;

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{ 7.81**2+17.46**2-15.62**2 }{ 2 * 7.81 * 17.46 } ) = 63° 27'33" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 15.62**2+17.46**2-7.81**2 }{ 2 * 15.62 * 17.46 } ) = 26° 34'16" ; ; gamma = 180° - alpha - beta = 180° - 63° 27'33" - 26° 34'16" = 89° 58'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 61 }{ 20.45 } = 2.98 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 15.62 }{ 2 * sin 63° 27'33" } = 8.73 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.81**2+2 * 17.46**2 - 15.62**2 } }{ 2 } = 11.042 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 17.46**2+2 * 15.62**2 - 7.81**2 } }{ 2 } = 16.099 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.81**2+2 * 15.62**2 - 17.46**2 } }{ 2 } = 8.734 ; ;
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