110 105 145 triangle

Acute scalene triangle.

Sides: a = 110   b = 105   c = 145

Area: T = 5751.08768538
Perimeter: p = 360
Semiperimeter: s = 180

Angle ∠ A = α = 49.06772754258° = 49°4'2″ = 0.85663855112 rad
Angle ∠ B = β = 46.14986331446° = 46°8'55″ = 0.80554455937 rad
Angle ∠ C = γ = 84.78440914295° = 84°47'3″ = 1.48797615488 rad

Height: ha = 104.5655215524
Height: hb = 109.5454511501
Height: hc = 79.32553359145

Median: ma = 114.018754251
Median: mb = 117.5
Median: mc = 79.41219008713

Inradius: r = 31.95504825211
Circumradius: R = 72.80114566017

Vertex coordinates: A[145; 0] B[0; 0] C[76.20768965517; 79.32553359145]
Centroid: CG[73.73656321839; 26.44217786382]
Coordinates of the circumscribed circle: U[72.5; 6.61883142365]
Coordinates of the inscribed circle: I[75; 31.95504825211]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.9332724574° = 130°55'58″ = 0.85663855112 rad
∠ B' = β' = 133.8511366855° = 133°51'5″ = 0.80554455937 rad
∠ C' = γ' = 95.21659085705° = 95°12'57″ = 1.48797615488 rad

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How did we calculate this triangle?

a = 110 ; ; b = 105 ; ; c = 145 ; ;

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

p = a+b+c = 110+105+145 = 360 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 360 }{ 2 } = 180 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 180 * (180-110)(180-105)(180-145) } ; ; T = sqrt{ 33075000 } = 5751.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5751.09 }{ 110 } = 104.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5751.09 }{ 105 } = 109.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5751.09 }{ 145 } = 79.33 ; ;

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{ 110**2-105**2-145**2 }{ 2 * 105 * 145 } ) = 49° 4'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 105**2-110**2-145**2 }{ 2 * 110 * 145 } ) = 46° 8'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 145**2-110**2-105**2 }{ 2 * 105 * 110 } ) = 84° 47'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5751.09 }{ 180 } = 31.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 110 }{ 2 * sin 49° 4'2" } = 72.8 ; ;




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