Triangle calculator

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

You have entered side a, b and c.

Obtuse isosceles triangle.

Sides: a = 4.5   b = 4.5   c = 6.64

Area: T = 10.08551523657
Perimeter: p = 15.64
Semiperimeter: s = 7.82

Angle ∠ A = α = 42.45875411892° = 42°27'27″ = 0.74110238861 rad
Angle ∠ B = β = 42.45875411892° = 42°27'27″ = 0.74110238861 rad
Angle ∠ C = γ = 95.08549176216° = 95°5'6″ = 1.66595448815 rad

Height: ha = 4.48222899403
Height: hb = 4.48222899403
Height: hc = 3.03876964957

Median: ma = 5.20664671323
Median: mb = 5.20664671323
Median: mc = 3.03876964957

Inradius: r = 1.29896614278
Circumradius: R = 3.33331177141

Vertex coordinates: A[6.64; 0] B[0; 0] C[3.32; 3.03876964957]
Centroid: CG[3.32; 1.01325654986]
Coordinates of the circumscribed circle: U[3.32; -0.29554212184]
Coordinates of the inscribed circle: I[3.32; 1.29896614278]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.5422458811° = 137°32'33″ = 0.74110238861 rad
∠ B' = β' = 137.5422458811° = 137°32'33″ = 0.74110238861 rad
∠ C' = γ' = 84.91550823784° = 84°54'54″ = 1.66595448815 rad

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How did we calculate this triangle?

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

a = 4.5 ; ; b = 4.5 ; ; c = 6.64 ; ;


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 = 4.5 ; ; b = 4.5 ; ; c = 6.64 ; ; : Nr. 1

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

p = a+b+c = 4.5+4.5+6.64 = 15.64 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.64 }{ 2 } = 7.82 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.82 * (7.82-4.5)(7.82-4.5)(7.82-6.64) } ; ; T = sqrt{ 101.71 } = 10.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10.09 }{ 4.5 } = 4.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10.09 }{ 4.5 } = 4.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10.09 }{ 6.64 } = 3.04 ; ;

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{ 4.5**2+6.64**2-4.5**2 }{ 2 * 4.5 * 6.64 } ) = 42° 27'27" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4.5**2+6.64**2-4.5**2 }{ 2 * 4.5 * 6.64 } ) = 42° 27'27" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 4.5**2+4.5**2-6.64**2 }{ 2 * 4.5 * 4.5 } ) = 95° 5'6" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10.09 }{ 7.82 } = 1.29 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4.5 }{ 2 * sin 42° 27'27" } = 3.33 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.5**2+2 * 6.64**2 - 4.5**2 } }{ 2 } = 5.206 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.64**2+2 * 4.5**2 - 4.5**2 } }{ 2 } = 5.206 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.5**2+2 * 4.5**2 - 6.64**2 } }{ 2 } = 3.038 ; ;
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