94 85 105 triangle

Acute scalene triangle.

Sides: a = 94   b = 85   c = 105

Area: T = 3791.433033696
Perimeter: p = 284
Semiperimeter: s = 142

Angle ∠ A = α = 58.17703889792° = 58°10'13″ = 1.01552648149 rad
Angle ∠ B = β = 50.19991139481° = 50°11'57″ = 0.876613982 rad
Angle ∠ C = γ = 71.63304970727° = 71°37'50″ = 1.25501880188 rad

Height: ha = 80.66987305736
Height: hb = 89.21101255755
Height: hc = 72.21877207039

Median: ma = 83.16224915452
Median: mb = 90.13546215391
Median: mc = 72.62440318352

Inradius: r = 26.77002136405
Circumradius: R = 55.31988325671

Vertex coordinates: A[105; 0] B[0; 0] C[60.17114285714; 72.21877207039]
Centroid: CG[55.05771428571; 24.0732573568]
Coordinates of the circumscribed circle: U[52.5; 17.43333942934]
Coordinates of the inscribed circle: I[57; 26.77002136405]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.8329611021° = 121°49'47″ = 1.01552648149 rad
∠ B' = β' = 129.8010886052° = 129°48'3″ = 0.876613982 rad
∠ C' = γ' = 108.3769502927° = 108°22'10″ = 1.25501880188 rad

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How did we calculate this triangle?

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

p = a+b+c = 94+85+105 = 284 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 284 }{ 2 } = 142 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 142 * (142-94)(142-85)(142-105) } ; ; T = sqrt{ 14374944 } = 3791.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3791.43 }{ 94 } = 80.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3791.43 }{ 85 } = 89.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3791.43 }{ 105 } = 72.22 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 85**2+105**2-94**2 }{ 2 * 85 * 105 } ) = 58° 10'13" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 94**2+105**2-85**2 }{ 2 * 94 * 105 } ) = 50° 11'57" ; ;
 gamma = 180° - alpha - beta = 180° - 58° 10'13" - 50° 11'57" = 71° 37'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3791.43 }{ 142 } = 26.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 94 }{ 2 * sin 58° 10'13" } = 55.32 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 85**2+2 * 105**2 - 94**2 } }{ 2 } = 83.162 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 105**2+2 * 94**2 - 85**2 } }{ 2 } = 90.135 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 85**2+2 * 94**2 - 105**2 } }{ 2 } = 72.624 ; ;
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