37 34 65.35 triangle

Obtuse scalene triangle.

Sides: a = 37   b = 34   c = 65.35

Area: T = 452.9880276026
Perimeter: p = 136.35
Semiperimeter: s = 68.175

Angle ∠ A = α = 24.06330300085° = 24°3'47″ = 0.42199791017 rad
Angle ∠ B = β = 22.00546141187° = 22°17″ = 0.3844052967 rad
Angle ∠ C = γ = 133.9322355873° = 133°55'56″ = 2.33875605849 rad

Height: ha = 24.48554203257
Height: hb = 26.64658985897
Height: hc = 13.86332066113

Median: ma = 48.69435442333
Median: mb = 50.30771689722
Median: mc = 13.95986666627

Inradius: r = 6.64443751526
Circumradius: R = 45.37218982652

Vertex coordinates: A[65.35; 0] B[0; 0] C[34.30546863045; 13.86332066113]
Centroid: CG[33.21882287682; 4.62110688704]
Coordinates of the circumscribed circle: U[32.675; -31.479941434]
Coordinates of the inscribed circle: I[34.175; 6.64443751526]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.9376969992° = 155°56'13″ = 0.42199791017 rad
∠ B' = β' = 157.9955385881° = 157°59'43″ = 0.3844052967 rad
∠ C' = γ' = 46.06876441272° = 46°4'4″ = 2.33875605849 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 = 37 ; ; b = 34 ; ; c = 65.35 ; ;

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

p = a+b+c = 37+34+65.35 = 136.35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 136.35 }{ 2 } = 68.18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 68.18 * (68.18-37)(68.18-34)(68.18-65.35) } ; ; T = sqrt{ 205191.13 } = 452.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 452.98 }{ 37 } = 24.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 452.98 }{ 34 } = 26.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 452.98 }{ 65.35 } = 13.86 ; ;

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{ 34**2+65.35**2-37**2 }{ 2 * 34 * 65.35 } ) = 24° 3'47" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 37**2+65.35**2-34**2 }{ 2 * 37 * 65.35 } ) = 22° 17" ; ;
 gamma = 180° - alpha - beta = 180° - 24° 3'47" - 22° 17" = 133° 55'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 452.98 }{ 68.18 } = 6.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 37 }{ 2 * sin 24° 3'47" } = 45.37 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 34**2+2 * 65.35**2 - 37**2 } }{ 2 } = 48.694 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 65.35**2+2 * 37**2 - 34**2 } }{ 2 } = 50.307 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 34**2+2 * 37**2 - 65.35**2 } }{ 2 } = 13.959 ; ;
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