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 = 1060   b = 851   c = 904

Area: T = 370197.881054625
Perimeter: p = 2815
Semiperimeter: s = 1407.5

Angle ∠ A = α = 74.24331688342° = 74°14'35″ = 1.29657877433 rad
Angle ∠ B = β = 50.59435515431° = 50°35'37″ = 0.88330240547 rad
Angle ∠ C = γ = 55.16332796226° = 55°9'48″ = 0.96327808556 rad

Height: ha = 698.48765670684
Height: hb = 870.03302715541
Height: hc = 819.02218596156

Median: ma = 699.86332009186
Median: mb = 888.45880744188
Median: mc = 848.29903394475

Inradius: r = 263.01880323597
Circumradius: R = 550.69334823592

Vertex coordinates: A[904; 0] B[0; 0] C[672.90765265487; 819.02218596156]
Centroid: CG[525.63655088496; 273.00772865385]
Coordinates of the circumscribed circle: U[452; 314.57879895556]
Coordinates of the inscribed circle: I[556.5; 263.01880323597]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 105.75768311658° = 105°45'25″ = 1.29657877433 rad
∠ B' = β' = 129.40664484569° = 129°24'23″ = 0.88330240547 rad
∠ C' = γ' = 124.83767203774° = 124°50'12″ = 0.96327808556 rad

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How did we calculate this triangle?

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

a = 1060 ; ; b = 851 ; ; c = 904 ; ;


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 = 1060 ; ; b = 851 ; ; c = 904 ; ; : Nr. 1

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

p = a+b+c = 1060+851+904 = 2815 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2815 }{ 2 } = 1407.5 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1407.5 * (1407.5-1060)(1407.5-851)(1407.5-904) } ; ; T = sqrt{ 137046470760.94 } = 370197.88 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 370197.88 }{ 1060 } = 698.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 370197.88 }{ 851 } = 870.03 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 370197.88 }{ 904 } = 819.02 ; ;

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{ 851**2+904**2-1060**2 }{ 2 * 851 * 904 } ) = 74° 14'35" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1060**2+904**2-851**2 }{ 2 * 1060 * 904 } ) = 50° 35'37" ; ; gamma = 180° - alpha - beta = 180° - 74° 14'35" - 50° 35'37" = 55° 9'48" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 370197.88 }{ 1407.5 } = 263.02 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1060 }{ 2 * sin 74° 14'35" } = 550.69 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 851**2+2 * 904**2 - 1060**2 } }{ 2 } = 699.863 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 904**2+2 * 1060**2 - 851**2 } }{ 2 } = 888.458 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 851**2+2 * 1060**2 - 904**2 } }{ 2 } = 848.29 ; ;
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