Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 6.40331242374   b = 2.23660679775   c = 4.4722135955

Area: T = 3
Perimeter: p = 13.11113281699
Semiperimeter: s = 6.5565664085

Angle ∠ A = α = 143.1330102354° = 143°7'48″ = 2.49880915448 rad
Angle ∠ B = β = 12.0954757077° = 12°5'41″ = 0.21110933332 rad
Angle ∠ C = γ = 24.77551405688° = 24°46'31″ = 0.43224077756 rad

Height: ha = 0.93770425713
Height: hb = 2.6833281573
Height: hc = 1.34216407865

Median: ma = 1.5
Median: mb = 5.40883269132
Median: mc = 4.24326406871

Inradius: r = 0.45876195426
Circumradius: R = 5.33659368645

Vertex coordinates: A[0; 0] B[-2; 4] C[2; -1]
Centroid: CG[0; 1]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[2.13655578655; 0.45876195426]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 36.87698976458° = 36°52'12″ = 2.49880915448 rad
∠ B' = β' = 167.9055242923° = 167°54'19″ = 0.21110933332 rad
∠ C' = γ' = 155.2254859431° = 155°13'29″ = 0.43224077756 rad

Calculate another triangle




How did we calculate this triangle?

1. We compute side a from coordinates using the Pythagorean theorem

a = | beta gamma | = | beta - gamma | ; ; a**2 = ( beta _x- gamma _x)**2 + ( beta _y- gamma _y)**2 ; ; a = sqrt{ ( beta _x- gamma _x)**2 + ( beta _y- gamma _y)**2 } ; ; a = sqrt{ (-2-2)**2 + (4-(-1))**2 } ; ; a = sqrt{ 41 } = 6.4 ; ;

2. We compute side b from coordinates using the Pythagorean theorem

b = | alpha gamma | = | alpha - gamma | ; ; b**2 = ( alpha _x- gamma _x)**2 + ( alpha _y- gamma _y)**2 ; ; b = sqrt{ ( alpha _x- gamma _x)**2 + ( alpha _y- gamma _y)**2 } ; ; b = sqrt{ (0-2)**2 + (0-(-1))**2 } ; ; b = sqrt{ 5 } = 2.24 ; ;

3. We compute side c from coordinates using the Pythagorean theorem

c = | alpha beta | = | alpha - beta | ; ; c**2 = ( alpha _x- beta _x)**2 + ( alpha _y- beta _y)**2 ; ; c = sqrt{ ( alpha _x- beta _x)**2 + ( alpha _y- beta _y)**2 } ; ; c = sqrt{ (0-(-2))**2 + (0-4)**2 } ; ; c = sqrt{ 20 } = 4.47 ; ;


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 = 6.4 ; ; b = 2.24 ; ; c = 4.47 ; ;

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

p = a+b+c = 6.4+2.24+4.47 = 13.11 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13.11 }{ 2 } = 6.56 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.56 * (6.56-6.4)(6.56-2.24)(6.56-4.47) } ; ; T = sqrt{ 9 } = 3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3 }{ 6.4 } = 0.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3 }{ 2.24 } = 2.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3 }{ 4.47 } = 1.34 ; ;

8. 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{ 6.4**2-2.24**2-4.47**2 }{ 2 * 2.24 * 4.47 } ) = 143° 7'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2.24**2-6.4**2-4.47**2 }{ 2 * 6.4 * 4.47 } ) = 12° 5'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4.47**2-6.4**2-2.24**2 }{ 2 * 2.24 * 6.4 } ) = 24° 46'31" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3 }{ 6.56 } = 0.46 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.4 }{ 2 * sin 143° 7'48" } = 5.34 ; ;




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