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 = 6.5   b = 14.1   c = 10.2

Area: T = 30.43988830281
Perimeter: p = 30.8
Semiperimeter: s = 15.4

Angle ∠ A = α = 25.04325610751° = 25°2'33″ = 0.43770751439 rad
Angle ∠ B = β = 113.3333250051° = 113°20' = 1.97880383654 rad
Angle ∠ C = γ = 41.62441888734° = 41°37'27″ = 0.72664791443 rad

Height: ha = 9.36658101625
Height: hb = 4.31875720607
Height: hc = 5.96884084369

Median: ma = 11.86985508804
Median: mb = 4.8421745553
Median: mc = 9.72221396822

Inradius: r = 1.9776550846
Circumradius: R = 7.67879262821

Vertex coordinates: A[10.2; 0] B[0; 0] C[-2.57545098039; 5.96884084369]
Centroid: CG[2.54218300654; 1.9899469479]
Coordinates of the circumscribed circle: U[5.1; 5.73993860293]
Coordinates of the inscribed circle: I[1.3; 1.9776550846]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.9577438925° = 154°57'27″ = 0.43770751439 rad
∠ B' = β' = 66.66767499485° = 66°40' = 1.97880383654 rad
∠ C' = γ' = 138.3765811127° = 138°22'33″ = 0.72664791443 rad

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How did we calculate this triangle?

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 = 6.5 ; ; b = 14.1 ; ; c = 10.2 ; ;

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

p = a+b+c = 6.5+14.1+10.2 = 30.8 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 30.8 }{ 2 } = 15.4 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.4 * (15.4-6.5)(15.4-14.1)(15.4-10.2) } ; ; T = sqrt{ 926.53 } = 30.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 30.44 }{ 6.5 } = 9.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 30.44 }{ 14.1 } = 4.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 30.44 }{ 10.2 } = 5.97 ; ;

5. 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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 6.5**2-14.1**2-10.2**2 }{ 2 * 14.1 * 10.2 } ) = 25° 2'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14.1**2-6.5**2-10.2**2 }{ 2 * 6.5 * 10.2 } ) = 113° 20' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10.2**2-6.5**2-14.1**2 }{ 2 * 14.1 * 6.5 } ) = 41° 37'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 30.44 }{ 15.4 } = 1.98 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.5 }{ 2 * sin 25° 2'33" } = 7.68 ; ;




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