48.5 36 60 triangle

Acute scalene triangle.

Sides: a = 48.5   b = 36   c = 60

Area: T = 872.9176660451
Perimeter: p = 144.5
Semiperimeter: s = 72.25

Angle ∠ A = α = 53.92659024583° = 53°55'33″ = 0.941118455 rad
Angle ∠ B = β = 36.86657955185° = 36°51'57″ = 0.64334295132 rad
Angle ∠ C = γ = 89.20883020232° = 89°12'30″ = 1.55769785904 rad

Height: ha = 35.99765633176
Height: hb = 48.49553700251
Height: hc = 29.0977222015

Median: ma = 43.12769927076
Median: mb = 51.49987863935
Median: mc = 30.39994243367

Inradius: r = 12.08218914941
Circumradius: R = 30.00328641754

Vertex coordinates: A[60; 0] B[0; 0] C[38.80220833333; 29.0977222015]
Centroid: CG[32.93440277778; 9.6999074005]
Coordinates of the circumscribed circle: U[30; 0.41545584755]
Coordinates of the inscribed circle: I[36.25; 12.08218914941]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.0744097542° = 126°4'27″ = 0.941118455 rad
∠ B' = β' = 143.1344204481° = 143°8'3″ = 0.64334295132 rad
∠ C' = γ' = 90.79216979768° = 90°47'30″ = 1.55769785904 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 = 48.5 ; ; b = 36 ; ; c = 60 ; ;

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

p = a+b+c = 48.5+36+60 = 144.5 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 144.5 }{ 2 } = 72.25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 72.25 * (72.25-48.5)(72.25-36)(72.25-60) } ; ; T = sqrt{ 761983.5 } = 872.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 872.92 }{ 48.5 } = 36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 872.92 }{ 36 } = 48.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 872.92 }{ 60 } = 29.1 ; ;

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{ 48.5**2-36**2-60**2 }{ 2 * 36 * 60 } ) = 53° 55'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 36**2-48.5**2-60**2 }{ 2 * 48.5 * 60 } ) = 36° 51'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 60**2-48.5**2-36**2 }{ 2 * 36 * 48.5 } ) = 89° 12'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 872.92 }{ 72.25 } = 12.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 48.5 }{ 2 * sin 53° 55'33" } = 30 ; ;




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