35 52 82 triangle

Obtuse scalene triangle.

Sides: a = 35   b = 52   c = 82

Area: T = 582.9655211226
Perimeter: p = 169
Semiperimeter: s = 84.5

Angle ∠ A = α = 15.86988221166° = 15°52'8″ = 0.27769631943 rad
Angle ∠ B = β = 23.9699327689° = 23°58'10″ = 0.41883436877 rad
Angle ∠ C = γ = 140.1621850194° = 140°9'43″ = 2.44662857716 rad

Height: ha = 33.31222977844
Height: hb = 22.42217388933
Height: hc = 14.21986636884

Median: ma = 66.3910887929
Median: mb = 57.43325691572
Median: mc = 16.83774582405

Inradius: r = 6.89989965826
Circumradius: R = 644.0003884992

Vertex coordinates: A[82; 0] B[0; 0] C[31.98217073171; 14.21986636884]
Centroid: CG[37.9943902439; 4.74395545628]
Coordinates of the circumscribed circle: U[41; -49.14331554548]
Coordinates of the inscribed circle: I[32.5; 6.89989965826]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.1311177883° = 164°7'52″ = 0.27769631943 rad
∠ B' = β' = 156.0310672311° = 156°1'50″ = 0.41883436877 rad
∠ C' = γ' = 39.83881498056° = 39°50'17″ = 2.44662857716 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 = 35+52+82 = 169 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 169 }{ 2 } = 84.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 84.5 * (84.5-35)(84.5-52)(84.5-82) } ; ; T = sqrt{ 339848.44 } = 582.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 582.97 }{ 35 } = 33.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 582.97 }{ 52 } = 22.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 582.97 }{ 82 } = 14.22 ; ;

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{ 52**2+82**2-35**2 }{ 2 * 52 * 82 } ) = 15° 52'8" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 35**2+82**2-52**2 }{ 2 * 35 * 82 } ) = 23° 58'10" ; ; gamma = 180° - alpha - beta = 180° - 15° 52'8" - 23° 58'10" = 140° 9'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 582.97 }{ 84.5 } = 6.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 35 }{ 2 * sin 15° 52'8" } = 64 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 52**2+2 * 82**2 - 35**2 } }{ 2 } = 66.391 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 82**2+2 * 35**2 - 52**2 } }{ 2 } = 57.433 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 52**2+2 * 35**2 - 82**2 } }{ 2 } = 16.837 ; ;
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