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 = 174   b = 185   c = 152

Area: T = 12326.47875762
Perimeter: p = 511
Semiperimeter: s = 255.5

Angle ∠ A = α = 61.24774532473° = 61°14'51″ = 1.06989697176 rad
Angle ∠ B = β = 68.76992011386° = 68°46'9″ = 1.22002489838 rad
Angle ∠ C = γ = 49.98333456141° = 49°59' = 0.87223739521 rad

Height: ha = 141.6843650302
Height: hb = 133.259921704
Height: hc = 162.1990494424

Median: ma = 145.2432899999
Median: mb = 134.6621612942
Median: mc = 162.7109864483

Inradius: r = 48.24545306311
Circumradius: R = 99.23551620675

Vertex coordinates: A[152; 0] B[0; 0] C[63.01098684211; 162.1990494424]
Centroid: CG[71.67699561404; 54.06334981414]
Coordinates of the circumscribed circle: U[76; 63.80992265317]
Coordinates of the inscribed circle: I[70.5; 48.24545306311]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 118.7532546753° = 118°45'9″ = 1.06989697176 rad
∠ B' = β' = 111.2310798861° = 111°13'51″ = 1.22002489838 rad
∠ C' = γ' = 130.0176654386° = 130°1' = 0.87223739521 rad

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How did we calculate this triangle?

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

a = 174 ; ; b = 185 ; ; c = 152 ; ;

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

p = a+b+c = 174+185+152 = 511 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 511 }{ 2 } = 255.5 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 255.5 * (255.5-174)(255.5-185)(255.5-152) } ; ; T = sqrt{ 151942049.44 } = 12326.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12326.48 }{ 174 } = 141.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12326.48 }{ 185 } = 133.26 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12326.48 }{ 152 } = 162.19 ; ;

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{ 185**2+152**2-174**2 }{ 2 * 185 * 152 } ) = 61° 14'51" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 174**2+152**2-185**2 }{ 2 * 174 * 152 } ) = 68° 46'9" ; ; gamma = 180° - alpha - beta = 180° - 61° 14'51" - 68° 46'9" = 49° 59' ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12326.48 }{ 255.5 } = 48.24 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 174 }{ 2 * sin 61° 14'51" } = 99.24 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 185**2+2 * 152**2 - 174**2 } }{ 2 } = 145.243 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 152**2+2 * 174**2 - 185**2 } }{ 2 } = 134.662 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 185**2+2 * 174**2 - 152**2 } }{ 2 } = 162.71 ; ;
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