Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and c.

Acute scalene triangle.

Sides: a = 554   b = 541   c = 470

Area: T = 116163.2776624
Perimeter: p = 1565
Semiperimeter: s = 782.5

Angle ∠ A = α = 66.02218092982° = 66°1'19″ = 1.15222979504 rad
Angle ∠ B = β = 63.15985743763° = 63°9'31″ = 1.10223250737 rad
Angle ∠ C = γ = 50.82196163254° = 50°49'11″ = 0.88769696295 rad

Height: ha = 419.3622009472
Height: hb = 429.4399100272
Height: hc = 494.312181542

Median: ma = 424.3376540967
Median: mb = 436.7355331751
Median: mc = 494.5443729108

Inradius: r = 148.4511471723
Circumradius: R = 303.1632892986

Vertex coordinates: A[470; 0] B[0; 0] C[250.1443617021; 494.312181542]
Centroid: CG[240.048787234; 164.771060514]
Coordinates of the circumscribed circle: U[235; 191.527738625]
Coordinates of the inscribed circle: I[241.5; 148.4511471723]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 113.9788190702° = 113°58'41″ = 1.15222979504 rad
∠ B' = β' = 116.8411425624° = 116°50'29″ = 1.10223250737 rad
∠ C' = γ' = 129.1880383675° = 129°10'49″ = 0.88769696295 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c.

a = 554 ; ; b = 541 ; ; c = 470 ; ;


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 = 554 ; ; b = 541 ; ; c = 470 ; ; : Nr. 1

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

p = a+b+c = 554+541+470 = 1565 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1565 }{ 2 } = 782.5 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 782.5 * (782.5-554)(782.5-541)(782.5-470) } ; ; T = sqrt{ 13493906835.9 } = 116163.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 116163.28 }{ 554 } = 419.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 116163.28 }{ 541 } = 429.44 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 116163.28 }{ 470 } = 494.31 ; ;

6. 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{ 541**2+470**2-554**2 }{ 2 * 541 * 470 } ) = 66° 1'19" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 554**2+470**2-541**2 }{ 2 * 554 * 470 } ) = 63° 9'31" ; ; gamma = 180° - alpha - beta = 180° - 66° 1'19" - 63° 9'31" = 50° 49'11" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 116163.28 }{ 782.5 } = 148.45 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 554 }{ 2 * sin 66° 1'19" } = 303.16 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 541**2+2 * 470**2 - 554**2 } }{ 2 } = 424.337 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 470**2+2 * 554**2 - 541**2 } }{ 2 } = 436.735 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 541**2+2 * 554**2 - 470**2 } }{ 2 } = 494.544 ; ;
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