Triangle calculator VC

Please enter the coordinates of the three vertices


Acute isosceles triangle.

Sides: a = 8.24662112512   b = 8.48552813742   c = 8.24662112512

Area: T = 30
Perimeter: p = 24.97877038767
Semiperimeter: s = 12.48988519384

Angle ∠ A = α = 59.03662434679° = 59°2'10″ = 1.03303768265 rad
Angle ∠ B = β = 61.92875130641° = 61°55'39″ = 1.08108390005 rad
Angle ∠ C = γ = 59.03662434679° = 59°2'10″ = 1.03303768265 rad

Height: ha = 7.27660687511
Height: hb = 7.07110678119
Height: hc = 7.27660687511

Median: ma = 7.28801098893
Median: mb = 7.07110678119
Median: mc = 7.28801098893

Inradius: r = 2.40221423385
Circumradius: R = 4.80883261121

Vertex coordinates: A[-7; -7] B[-9; 1] C[-1; -1]
Centroid: CG[-5.66766666667; -2.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.28111425805; 2.40221423385]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120.9643756532° = 120°57'50″ = 1.03303768265 rad
∠ B' = β' = 118.0722486936° = 118°4'21″ = 1.08108390005 rad
∠ C' = γ' = 120.9643756532° = 120°57'50″ = 1.03303768265 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{ (-9-(-1))**2 + (1-(-1))**2 } ; ; a = sqrt{ 68 } = 8.25 ; ;

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-(-1))**2 + (-7-(-1))**2 } ; ; b = sqrt{ 72 } = 8.49 ; ;

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-(-9))**2 + (-7-1)**2 } ; ; c = sqrt{ 68 } = 8.25 ; ;


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 = 8.25 ; ; b = 8.49 ; ; c = 8.25 ; ;

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

p = a+b+c = 8.25+8.49+8.25 = 24.98 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24.98 }{ 2 } = 12.49 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.49 * (12.49-8.25)(12.49-8.49)(12.49-8.25) } ; ; T = sqrt{ 900 } = 30 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 30 }{ 8.25 } = 7.28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 30 }{ 8.49 } = 7.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 30 }{ 8.25 } = 7.28 ; ;

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{ 8.25**2-8.49**2-8.25**2 }{ 2 * 8.49 * 8.25 } ) = 59° 2'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8.49**2-8.25**2-8.25**2 }{ 2 * 8.25 * 8.25 } ) = 61° 55'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8.25**2-8.25**2-8.49**2 }{ 2 * 8.49 * 8.25 } ) = 59° 2'10" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 30 }{ 12.49 } = 2.4 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8.25 }{ 2 * sin 59° 2'10" } = 4.81 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.