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 = 177   b = 118   c = 171

Area: T = 9645.322218228
Perimeter: p = 466
Semiperimeter: s = 233

Angle ∠ A = α = 72.94549901151° = 72°56'42″ = 1.27331302503 rad
Angle ∠ B = β = 39.59444293056° = 39°35'40″ = 0.69110531568 rad
Angle ∠ C = γ = 67.46105805793° = 67°27'38″ = 1.17774092464 rad

Height: ha = 108.9876691325
Height: hb = 163.4880036988
Height: hc = 112.8110785758

Median: ma = 117.2611459994
Median: mb = 163.7199271926
Median: mc = 123.7598838068

Inradius: r = 41.3966232542
Circumradius: R = 92.57109357475

Vertex coordinates: A[171; 0] B[0; 0] C[136.3921812865; 112.8110785758]
Centroid: CG[102.4643937622; 37.60435952526]
Coordinates of the circumscribed circle: U[85.5; 35.48441957098]
Coordinates of the inscribed circle: I[115; 41.3966232542]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 107.0555009885° = 107°3'18″ = 1.27331302503 rad
∠ B' = β' = 140.4065570694° = 140°24'20″ = 0.69110531568 rad
∠ C' = γ' = 112.5399419421° = 112°32'22″ = 1.17774092464 rad

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How did we calculate this triangle?

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

a = 177 ; ; b = 118 ; ; c = 171 ; ;

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

p = a+b+c = 177+118+171 = 466 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 466 }{ 2 } = 233 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 233 * (233-177)(233-118)(233-171) } ; ; T = sqrt{ 93032240 } = 9645.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9645.32 }{ 177 } = 108.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9645.32 }{ 118 } = 163.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9645.32 }{ 171 } = 112.81 ; ;

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{ 118**2+171**2-177**2 }{ 2 * 118 * 171 } ) = 72° 56'42" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 177**2+171**2-118**2 }{ 2 * 177 * 171 } ) = 39° 35'40" ; ;
 gamma = 180° - alpha - beta = 180° - 72° 56'42" - 39° 35'40" = 67° 27'38" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9645.32 }{ 233 } = 41.4 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 177 }{ 2 * sin 72° 56'42" } = 92.57 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 118**2+2 * 171**2 - 177**2 } }{ 2 } = 117.261 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 171**2+2 * 177**2 - 118**2 } }{ 2 } = 163.719 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 118**2+2 * 177**2 - 171**2 } }{ 2 } = 123.759 ; ;
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