164 145 89 triangle

Acute scalene triangle.

Sides: a = 164   b = 145   c = 89

Area: T = 6432.115473778
Perimeter: p = 398
Semiperimeter: s = 199

Angle ∠ A = α = 85.44443937593° = 85°26'40″ = 1.49112859985 rad
Angle ∠ B = β = 61.80660172058° = 61°48'22″ = 1.07987184978 rad
Angle ∠ C = γ = 32.75495890349° = 32°44'59″ = 0.57215881573 rad

Height: ha = 78.44404236315
Height: hb = 88.71988239694
Height: hc = 144.542190422

Median: ma = 88.02884045067
Median: mb = 110.237724416
Median: mc = 148.2577377557

Inradius: r = 32.3222184612
Circumradius: R = 82.26598821025

Vertex coordinates: A[89; 0] B[0; 0] C[77.48331460674; 144.542190422]
Centroid: CG[55.49443820225; 48.18106347399]
Coordinates of the circumscribed circle: U[44.5; 69.18440892368]
Coordinates of the inscribed circle: I[54; 32.3222184612]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 94.55656062407° = 94°33'20″ = 1.49112859985 rad
∠ B' = β' = 118.1943982794° = 118°11'38″ = 1.07987184978 rad
∠ C' = γ' = 147.2550410965° = 147°15'1″ = 0.57215881573 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 = 164 ; ; b = 145 ; ; c = 89 ; ;

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

p = a+b+c = 164+145+89 = 398 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 398 }{ 2 } = 199 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 199 * (199-164)(199-145)(199-89) } ; ; T = sqrt{ 41372100 } = 6432.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6432.11 }{ 164 } = 78.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6432.11 }{ 145 } = 88.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6432.11 }{ 89 } = 144.54 ; ;

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{ 164**2-145**2-89**2 }{ 2 * 145 * 89 } ) = 85° 26'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 145**2-164**2-89**2 }{ 2 * 164 * 89 } ) = 61° 48'22" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 89**2-164**2-145**2 }{ 2 * 145 * 164 } ) = 32° 44'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6432.11 }{ 199 } = 32.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 164 }{ 2 * sin 85° 26'40" } = 82.26 ; ;




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