Triangle calculator

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

You have entered side a, b and c.

Acute isosceles triangle.

Sides: a = 487.5   b = 487.5   c = 635

Area: T = 117453.5455338
Perimeter: p = 1610
Semiperimeter: s = 805

Angle ∠ A = α = 49.36216670713° = 49°21'42″ = 0.86215236147 rad
Angle ∠ B = β = 49.36216670713° = 49°21'42″ = 0.86215236147 rad
Angle ∠ C = γ = 81.27766658574° = 81°16'36″ = 1.41985454243 rad

Height: ha = 481.8610698823
Height: hb = 481.8610698823
Height: hc = 369.9322426262

Median: ma = 510.9087587045
Median: mb = 510.9087587045
Median: mc = 369.9322426262

Inradius: r = 145.9055025265
Circumradius: R = 321.2165758783

Vertex coordinates: A[635; 0] B[0; 0] C[317.5; 369.9322426262]
Centroid: CG[317.5; 123.3110808754]
Coordinates of the circumscribed circle: U[317.5; 48.71766674793]
Coordinates of the inscribed circle: I[317.5; 145.9055025265]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.6388332929° = 130°38'18″ = 0.86215236147 rad
∠ B' = β' = 130.6388332929° = 130°38'18″ = 0.86215236147 rad
∠ C' = γ' = 98.72333341426° = 98°43'24″ = 1.41985454243 rad

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How did we calculate this triangle?

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

a = 487.5 ; ; b = 487.5 ; ; c = 635 ; ;

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

p = a+b+c = 487.5+487.5+635 = 1610 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1610 }{ 2 } = 805 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 805 * (805-487.5)(805-487.5)(805-635) } ; ; T = sqrt{ 13795335312.5 } = 117453.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 117453.55 }{ 487.5 } = 481.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 117453.55 }{ 487.5 } = 481.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 117453.55 }{ 635 } = 369.93 ; ;

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{ 487.5**2+635**2-487.5**2 }{ 2 * 487.5 * 635 } ) = 49° 21'42" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 487.5**2+635**2-487.5**2 }{ 2 * 487.5 * 635 } ) = 49° 21'42" ; ;
 gamma = 180° - alpha - beta = 180° - 49° 21'42" - 49° 21'42" = 81° 16'36" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 117453.55 }{ 805 } = 145.91 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 487.5 }{ 2 * sin 49° 21'42" } = 321.22 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 487.5**2+2 * 635**2 - 487.5**2 } }{ 2 } = 510.908 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 635**2+2 * 487.5**2 - 487.5**2 } }{ 2 } = 510.908 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 487.5**2+2 * 487.5**2 - 635**2 } }{ 2 } = 369.932 ; ;
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