Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse isosceles triangle.

Sides: a = 10.05498756211   b = 10.05498756211   c = 15.55663491861

Area: T = 49.5
Perimeter: p = 35.65661004283
Semiperimeter: s = 17.82880502142

Angle ∠ A = α = 39.28994068625° = 39°17'22″ = 0.68657295109 rad
Angle ∠ B = β = 39.28994068625° = 39°17'22″ = 0.68657295109 rad
Angle ∠ C = γ = 101.4211186275° = 101°25'16″ = 1.77701336318 rad

Height: ha = 9.85108681831
Height: hb = 9.85108681831
Height: hc = 6.36439610307

Median: ma = 12.09333866224
Median: mb = 12.09333866224
Median: mc = 6.36439610307

Inradius: r = 2.77765234788
Circumradius: R = 7.93553094333

Vertex coordinates: A[7; -2] B[-4; 9] C[-3; -1]
Centroid: CG[0; 2]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[3.39435286963; 2.77765234788]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.7110593137° = 140°42'38″ = 0.68657295109 rad
∠ B' = β' = 140.7110593137° = 140°42'38″ = 0.68657295109 rad
∠ C' = γ' = 78.5798813725° = 78°34'44″ = 1.77701336318 rad

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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{ (-4-(-3))**2 + (9-(-1))**2 } ; ; a = sqrt{ 101 } = 10.05 ; ;

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{ (7-(-3))**2 + (-2-(-1))**2 } ; ; b = sqrt{ 101 } = 10.05 ; ;

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{ (7-(-4))**2 + (-2-9)**2 } ; ; c = sqrt{ 242 } = 15.56 ; ;


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 = 10.05 ; ; b = 10.05 ; ; c = 15.56 ; ;

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

p = a+b+c = 10.05+10.05+15.56 = 35.66 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35.66 }{ 2 } = 17.83 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.83 * (17.83-10.05)(17.83-10.05)(17.83-15.56) } ; ; T = sqrt{ 2450.25 } = 49.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 49.5 }{ 10.05 } = 9.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 49.5 }{ 10.05 } = 9.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 49.5 }{ 15.56 } = 6.36 ; ;

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{ 10.05**2-10.05**2-15.56**2 }{ 2 * 10.05 * 15.56 } ) = 39° 17'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10.05**2-10.05**2-15.56**2 }{ 2 * 10.05 * 15.56 } ) = 39° 17'22" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15.56**2-10.05**2-10.05**2 }{ 2 * 10.05 * 10.05 } ) = 101° 25'16" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 49.5 }{ 17.83 } = 2.78 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10.05 }{ 2 * sin 39° 17'22" } = 7.94 ; ;




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