46 64 37 triangle

Obtuse scalene triangle.

Sides: a = 46   b = 64   c = 37

Area: T = 837.1798856338
Perimeter: p = 147
Semiperimeter: s = 73.5

Angle ∠ A = α = 44.99875655988° = 44°59'51″ = 0.78553556751 rad
Angle ∠ B = β = 100.3440329606° = 100°20'25″ = 1.75112691242 rad
Angle ∠ C = γ = 34.66221047953° = 34°39'44″ = 0.60549678543 rad

Height: ha = 36.39990807104
Height: hb = 26.16218392606
Height: hc = 45.25329111534

Median: ma = 46.94114528961
Median: mb = 26.80548503074
Median: mc = 52.57113800466

Inradius: r = 11.39901885216
Circumradius: R = 32.52882940364

Vertex coordinates: A[37; 0] B[0; 0] C[-8.25767567568; 45.25329111534]
Centroid: CG[9.58110810811; 15.08443037178]
Coordinates of the circumscribed circle: U[18.5; 26.75551847857]
Coordinates of the inscribed circle: I[9.5; 11.39901885216]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.0022434401° = 135°9″ = 0.78553556751 rad
∠ B' = β' = 79.66596703941° = 79°39'35″ = 1.75112691242 rad
∠ C' = γ' = 145.3387895205° = 145°20'16″ = 0.60549678543 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 = 46 ; ; b = 64 ; ; c = 37 ; ;

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

p = a+b+c = 46+64+37 = 147 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 147 }{ 2 } = 73.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 73.5 * (73.5-46)(73.5-64)(73.5-37) } ; ; T = sqrt{ 700868.44 } = 837.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 837.18 }{ 46 } = 36.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 837.18 }{ 64 } = 26.16 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 837.18 }{ 37 } = 45.25 ; ;

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{ 64**2+37**2-46**2 }{ 2 * 64 * 37 } ) = 44° 59'51" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 46**2+37**2-64**2 }{ 2 * 46 * 37 } ) = 100° 20'25" ; ; gamma = 180° - alpha - beta = 180° - 44° 59'51" - 100° 20'25" = 34° 39'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 837.18 }{ 73.5 } = 11.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 46 }{ 2 * sin 44° 59'51" } = 32.53 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 64**2+2 * 37**2 - 46**2 } }{ 2 } = 46.941 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 37**2+2 * 46**2 - 64**2 } }{ 2 } = 26.805 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 64**2+2 * 46**2 - 37**2 } }{ 2 } = 52.571 ; ;
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