104.25 162.25 192.25 triangle

Acute scalene triangle.

Sides: a = 104.25   b = 162.25   c = 192.25

Area: T = 8457.081053991
Perimeter: p = 458.75
Semiperimeter: s = 229.375

Angle ∠ A = α = 32.83769248653° = 32°50'13″ = 0.57331124551 rad
Angle ∠ B = β = 57.55878120145° = 57°33'28″ = 1.00545733299 rad
Angle ∠ C = γ = 89.60552631202° = 89°36'19″ = 1.56439068686 rad

Height: ha = 162.2466149447
Height: hb = 104.2487525916
Height: hc = 87.98800316246

Median: ma = 170.075512127
Median: mb = 131.6544080358
Median: mc = 96.72992451899

Inradius: r = 36.87701058961
Circumradius: R = 96.12772813141

Vertex coordinates: A[192.25; 0] B[0; 0] C[55.9254739922; 87.98800316246]
Centroid: CG[82.72549133073; 29.32766772082]
Coordinates of the circumscribed circle: U[96.125; 0.66222596506]
Coordinates of the inscribed circle: I[67.125; 36.87701058961]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.1633075135° = 147°9'47″ = 0.57331124551 rad
∠ B' = β' = 122.4422187985° = 122°26'32″ = 1.00545733299 rad
∠ C' = γ' = 90.39547368798° = 90°23'41″ = 1.56439068686 rad

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How did we calculate this triangle?

a = 104.25 ; ; b = 162.25 ; ; c = 192.25 ; ;

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

p = a+b+c = 104.25+162.25+192.25 = 458.75 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 458.75 }{ 2 } = 229.38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 229.38 * (229.38-104.25)(229.38-162.25)(229.38-192.25) } ; ; T = sqrt{ 71522211.26 } = 8457.08 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8457.08 }{ 104.25 } = 162.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8457.08 }{ 162.25 } = 104.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8457.08 }{ 192.25 } = 87.98 ; ;

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{ 104.25**2-162.25**2-192.25**2 }{ 2 * 162.25 * 192.25 } ) = 32° 50'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 162.25**2-104.25**2-192.25**2 }{ 2 * 104.25 * 192.25 } ) = 57° 33'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 192.25**2-104.25**2-162.25**2 }{ 2 * 162.25 * 104.25 } ) = 89° 36'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8457.08 }{ 229.38 } = 36.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 104.25 }{ 2 * sin 32° 50'13" } = 96.13 ; ;




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