35 560 562 triangle

Obtuse scalene triangle.

Sides: a = 35   b = 560   c = 562

Area: T = 9796.688834033
Perimeter: p = 1157
Semiperimeter: s = 578.5

Angle ∠ A = α = 3.56993449603° = 3°34'10″ = 0.06222968217 rad
Angle ∠ B = β = 84.94110893071° = 84°56'28″ = 1.48325016786 rad
Angle ∠ C = γ = 91.49895657326° = 91°29'22″ = 1.59767941533 rad

Height: ha = 559.8110762304
Height: hb = 34.9888172644
Height: hc = 34.86436595741

Median: ma = 560.7287875176
Median: mb = 283.0880377278
Median: mc = 280.0921949188

Inradius: r = 16.93546384448
Circumradius: R = 281.0954988871

Vertex coordinates: A[562; 0] B[0; 0] C[3.08662989324; 34.86436595741]
Centroid: CG[188.3622099644; 11.6211219858]
Coordinates of the circumscribed circle: U[281; -7.30770355525]
Coordinates of the inscribed circle: I[18.5; 16.93546384448]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.431065504° = 176°25'50″ = 0.06222968217 rad
∠ B' = β' = 95.05989106929° = 95°3'32″ = 1.48325016786 rad
∠ C' = γ' = 88.51104342674° = 88°30'38″ = 1.59767941533 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+560+562 = 1157 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1157 }{ 2 } = 578.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 578.5 * (578.5-35)(578.5-560)(578.5-562) } ; ; T = sqrt{ 95975102.44 } = 9796.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9796.69 }{ 35 } = 559.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9796.69 }{ 560 } = 34.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9796.69 }{ 562 } = 34.86 ; ;

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{ 560**2+562**2-35**2 }{ 2 * 560 * 562 } ) = 3° 34'10" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 35**2+562**2-560**2 }{ 2 * 35 * 562 } ) = 84° 56'28" ; ;
 gamma = 180° - alpha - beta = 180° - 3° 34'10" - 84° 56'28" = 91° 29'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9796.69 }{ 578.5 } = 16.93 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 35 }{ 2 * sin 3° 34'10" } = 281.09 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 560**2+2 * 562**2 - 35**2 } }{ 2 } = 560.728 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 562**2+2 * 35**2 - 560**2 } }{ 2 } = 283.08 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 560**2+2 * 35**2 - 562**2 } }{ 2 } = 280.092 ; ;
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