Triangle calculator

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

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 52   b = 81   c = 43

Area: T = 998.9599458637
Perimeter: p = 176
Semiperimeter: s = 88

Angle ∠ A = α = 35.00330563095° = 35°11″ = 0.61109185809 rad
Angle ∠ B = β = 116.6810575466° = 116°40'50″ = 2.0366460215 rad
Angle ∠ C = γ = 28.31663682245° = 28°18'59″ = 0.49442138577 rad

Height: ha = 38.42215176399
Height: hb = 24.66656656454
Height: hc = 46.46332306343

Median: ma = 59.40553869611
Median: mb = 25.22439965113
Median: mc = 64.57774728524

Inradius: r = 11.352181203
Circumradius: R = 45.32661637482

Vertex coordinates: A[43; 0] B[0; 0] C[-23.34988372093; 46.46332306343]
Centroid: CG[6.55503875969; 15.48877435448]
Coordinates of the circumscribed circle: U[21.5; 39.90325202228]
Coordinates of the inscribed circle: I[7; 11.352181203]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.997694369° = 144°59'49″ = 0.61109185809 rad
∠ B' = β' = 63.3199424534° = 63°19'10″ = 2.0366460215 rad
∠ C' = γ' = 151.6843631775° = 151°41'1″ = 0.49442138577 rad

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How did we calculate this triangle?

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

a = 52 ; ; b = 81 ; ; c = 43 ; ;


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 = 52 ; ; b = 81 ; ; c = 43 ; ; : Nr. 1

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

p = a+b+c = 52+81+43 = 176 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 176 }{ 2 } = 88 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 88 * (88-52)(88-81)(88-43) } ; ; T = sqrt{ 997920 } = 998.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 998.96 }{ 52 } = 38.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 998.96 }{ 81 } = 24.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 998.96 }{ 43 } = 46.46 ; ;

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{ 81**2+43**2-52**2 }{ 2 * 81 * 43 } ) = 35° 11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 52**2+43**2-81**2 }{ 2 * 52 * 43 } ) = 116° 40'50" ; ; gamma = 180° - alpha - beta = 180° - 35° 11" - 116° 40'50" = 28° 18'59" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 998.96 }{ 88 } = 11.35 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 52 }{ 2 * sin 35° 11" } = 45.33 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 81**2+2 * 43**2 - 52**2 } }{ 2 } = 59.405 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 43**2+2 * 52**2 - 81**2 } }{ 2 } = 25.224 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 81**2+2 * 52**2 - 43**2 } }{ 2 } = 64.577 ; ;
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