42 45 46 triangle

Acute scalene triangle.

Sides: a = 42   b = 45   c = 46

Area: T = 847.4033054927
Perimeter: p = 133
Semiperimeter: s = 66.5

Angle ∠ A = α = 54.96595509522° = 54°57'34″ = 0.95992251195 rad
Angle ∠ B = β = 61.31098651567° = 61°18'36″ = 1.07700590109 rad
Angle ∠ C = γ = 63.73105838912° = 63°43'50″ = 1.11223085231 rad

Height: ha = 40.35325264251
Height: hb = 37.66223579968
Height: hc = 36.84436110838

Median: ma = 40.36770657839
Median: mb = 37.86548913903
Median: mc = 36.95326724338

Inradius: r = 12.74329030816
Circumradius: R = 25.6498951669

Vertex coordinates: A[46; 0] B[0; 0] C[20.16330434783; 36.84436110838]
Centroid: CG[22.05443478261; 12.28112036946]
Coordinates of the circumscribed circle: U[23; 11.35220360165]
Coordinates of the inscribed circle: I[21.5; 12.74329030816]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.0440449048° = 125°2'26″ = 0.95992251195 rad
∠ B' = β' = 118.6990134843° = 118°41'24″ = 1.07700590109 rad
∠ C' = γ' = 116.2699416109° = 116°16'10″ = 1.11223085231 rad

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How did we calculate this triangle?

a = 42 ; ; b = 45 ; ; c = 46 ; ;

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

p = a+b+c = 42+45+46 = 133 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 133 }{ 2 } = 66.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 66.5 * (66.5-42)(66.5-45)(66.5-46) } ; ; T = sqrt{ 718091.94 } = 847.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 847.4 }{ 42 } = 40.35 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 847.4 }{ 45 } = 37.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 847.4 }{ 46 } = 36.84 ; ;

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{ 42**2-45**2-46**2 }{ 2 * 45 * 46 } ) = 54° 57'34" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 45**2-42**2-46**2 }{ 2 * 42 * 46 } ) = 61° 18'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 46**2-42**2-45**2 }{ 2 * 45 * 42 } ) = 63° 43'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 847.4 }{ 66.5 } = 12.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 42 }{ 2 * sin 54° 57'34" } = 25.65 ; ;




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