420 293 512 triangle

Acute scalene triangle.

Sides: a = 420   b = 293   c = 512

Area: T = 61529.99444006
Perimeter: p = 1225
Semiperimeter: s = 612.5

Angle ∠ A = α = 55.11660809659° = 55°6'58″ = 0.96219570837 rad
Angle ∠ B = β = 34.90883626268° = 34°54'30″ = 0.60992658643 rad
Angle ∠ C = γ = 89.97655564073° = 89°58'32″ = 1.57703697056 rad

Height: ha = 2932.999973336
Height: hb = 4209.999961779
Height: hc = 240.3521540627

Median: ma = 360.4121570292
Median: mb = 444.7588080309
Median: mc = 256.1032518535

Inradius: r = 100.4577133715
Circumradius: R = 2566.000023297

Vertex coordinates: A[512; 0] B[0; 0] C[344.4298710938; 240.3521540627]
Centroid: CG[285.4766236979; 80.11771802091]
Coordinates of the circumscribed circle: U[256; 0.1099215027]
Coordinates of the inscribed circle: I[319.5; 100.4577133715]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.8843919034° = 124°53'2″ = 0.96219570837 rad
∠ B' = β' = 145.0921637373° = 145°5'30″ = 0.60992658643 rad
∠ C' = γ' = 90.02444435927° = 90°1'28″ = 1.57703697056 rad

Calculate another triangle




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 = 420 ; ; b = 293 ; ; c = 512 ; ;

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

p = a+b+c = 420+293+512 = 1225 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1225 }{ 2 } = 612.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 612.5 * (612.5-420)(612.5-293)(612.5-512) } ; ; T = sqrt{ 3785940210.94 } = 61529.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 61529.99 }{ 420 } = 293 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 61529.99 }{ 293 } = 420 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 61529.99 }{ 512 } = 240.35 ; ;

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{ 293**2+512**2-420**2 }{ 2 * 293 * 512 } ) = 55° 6'58" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 420**2+512**2-293**2 }{ 2 * 420 * 512 } ) = 34° 54'30" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 420**2+293**2-512**2 }{ 2 * 420 * 293 } ) = 89° 58'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 61529.99 }{ 612.5 } = 100.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 420 }{ 2 * sin 55° 6'58" } = 256 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 293**2+2 * 512**2 - 420**2 } }{ 2 } = 360.412 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 512**2+2 * 420**2 - 293**2 } }{ 2 } = 444.758 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 293**2+2 * 420**2 - 512**2 } }{ 2 } = 256.103 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.