Triangle calculator VC

Please enter the coordinates of the three vertices


Right isosceles triangle.

Sides: a = 21.63333076528   b = 15.29770585408   c = 15.29770585408

Area: T = 117
Perimeter: p = 52.22774247343
Semiperimeter: s = 26.11437123672

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 45° = 0.78553981634 rad

Height: ha = 10.81766538264
Height: hb = 15.29770585408
Height: hc = 15.29770585408

Median: ma = 10.81766538264
Median: mb = 17.10326313765
Median: mc = 17.10326313765

Inradius: r = 4.48804047144
Circumradius: R = 10.81766538264

Vertex coordinates: A[4; 5] B[7; -10] C[-11; 2]
Centroid: CG[0; -1]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[4.48804047144; 4.48804047144]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 135° = 0.78553981634 rad
∠ C' = γ' = 135° = 0.78553981634 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{ (7-(-11))**2 + (-10-2)**2 } ; ; a = sqrt{ 468 } = 21.63 ; ;

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{ (4-(-11))**2 + (5-2)**2 } ; ; b = sqrt{ 234 } = 15.3 ; ;

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{ (4-7)**2 + (5-(-10))**2 } ; ; c = sqrt{ 234 } = 15.3 ; ;


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 = 21.63 ; ; b = 15.3 ; ; c = 15.3 ; ;

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

p = a+b+c = 21.63+15.3+15.3 = 52.23 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52.23 }{ 2 } = 26.11 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.11 * (26.11-21.63)(26.11-15.3)(26.11-15.3) } ; ; T = sqrt{ 13689 } = 117 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 117 }{ 21.63 } = 10.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 117 }{ 15.3 } = 15.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 117 }{ 15.3 } = 15.3 ; ;

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{ 21.63**2-15.3**2-15.3**2 }{ 2 * 15.3 * 15.3 } ) = 90° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15.3**2-21.63**2-15.3**2 }{ 2 * 21.63 * 15.3 } ) = 45° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15.3**2-21.63**2-15.3**2 }{ 2 * 15.3 * 21.63 } ) = 45° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 117 }{ 26.11 } = 4.48 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 21.63 }{ 2 * sin 90° } = 10.82 ; ;




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

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