Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 455   b = 495   c = 672

Area: T = 112612.4439739
Perimeter: p = 1622
Semiperimeter: s = 811

Angle ∠ A = α = 42.61661145003° = 42°36'58″ = 0.74437915124 rad
Angle ∠ B = β = 47.44331591994° = 47°26'35″ = 0.82880393356 rad
Angle ∠ C = γ = 89.94107263003° = 89°56'27″ = 1.57697618056 rad

Height: ha = 4954.999735117
Height: hb = 4554.999756522
Height: hc = 335.1566070652

Median: ma = 544.5622439028
Median: mb = 517.7343763628
Median: mc = 336.3476547477

Inradius: r = 138.8566275881
Circumradius: R = 3366.000179799

Vertex coordinates: A[672; 0] B[0; 0] C[307.7266190476; 335.1566070652]
Centroid: CG[326.5755396825; 111.7198690217]
Coordinates of the circumscribed circle: U[336; 0.34875992536]
Coordinates of the inscribed circle: I[316; 138.8566275881]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.38438855° = 137°23'2″ = 0.74437915124 rad
∠ B' = β' = 132.5576840801° = 132°33'25″ = 0.82880393356 rad
∠ C' = γ' = 90.05992736997° = 90°3'33″ = 1.57697618056 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 = 455+495+672 = 1622 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1622 }{ 2 } = 811 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 811 * (811-455)(811-495)(811-672) } ; ; T = sqrt{ 12681561584 } = 112612.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 112612.44 }{ 455 } = 495 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 112612.44 }{ 495 } = 455 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 112612.44 }{ 672 } = 335.16 ; ;

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{ 495**2+672**2-455**2 }{ 2 * 495 * 672 } ) = 42° 36'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 455**2+672**2-495**2 }{ 2 * 455 * 672 } ) = 47° 26'35" ; ; gamma = 180° - alpha - beta = 180° - 42° 36'58" - 47° 26'35" = 89° 56'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 112612.44 }{ 811 } = 138.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 455 }{ 2 * sin 42° 36'58" } = 336 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 495**2+2 * 672**2 - 455**2 } }{ 2 } = 544.562 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 672**2+2 * 455**2 - 495**2 } }{ 2 } = 517.734 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 495**2+2 * 455**2 - 672**2 } }{ 2 } = 336.347 ; ;
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