36 49 60 triangle

Acute scalene triangle.

Sides: a = 36   b = 49   c = 60

Area: T = 881.6676568211
Perimeter: p = 145
Semiperimeter: s = 72.5

Angle ∠ A = α = 36.85436542753° = 36°51'13″ = 0.64332176085 rad
Angle ∠ B = β = 54.72218533956° = 54°43'19″ = 0.95550765145 rad
Angle ∠ C = γ = 88.42444923291° = 88°25'28″ = 1.54332985305 rad

Height: ha = 48.98114760117
Height: hb = 35.98663905392
Height: hc = 29.3898885607

Median: ma = 51.7354901179
Median: mb = 42.98554626589
Median: mc = 30.79877271889

Inradius: r = 12.16109181822
Circumradius: R = 30.01113455064

Vertex coordinates: A[60; 0] B[0; 0] C[20.79216666667; 29.3898885607]
Centroid: CG[26.93105555556; 9.79662952023]
Coordinates of the circumscribed circle: U[30; 0.82551418691]
Coordinates of the inscribed circle: I[23.5; 12.16109181822]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1466345725° = 143°8'47″ = 0.64332176085 rad
∠ B' = β' = 125.2788146604° = 125°16'41″ = 0.95550765145 rad
∠ C' = γ' = 91.57655076709° = 91°34'32″ = 1.54332985305 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 = 36 ; ; b = 49 ; ; c = 60 ; ;

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

p = a+b+c = 36+49+60 = 145 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 145 }{ 2 } = 72.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 72.5 * (72.5-36)(72.5-49)(72.5-60) } ; ; T = sqrt{ 777335.94 } = 881.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 881.67 }{ 36 } = 48.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 881.67 }{ 49 } = 35.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 881.67 }{ 60 } = 29.39 ; ;

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{ 36**2-49**2-60**2 }{ 2 * 49 * 60 } ) = 36° 51'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 49**2-36**2-60**2 }{ 2 * 36 * 60 } ) = 54° 43'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 60**2-36**2-49**2 }{ 2 * 49 * 36 } ) = 88° 25'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 881.67 }{ 72.5 } = 12.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 36 }{ 2 * sin 36° 51'13" } = 30.01 ; ;




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