Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 18.02877563773   b = 8.6022325267   c = 10.44403065089

Area: T = 27.5
Perimeter: p = 37.07703881533
Semiperimeter: s = 18.53551940766

Angle ∠ A = α = 142.2376922026° = 142°14'13″ = 2.48325026073 rad
Angle ∠ B = β = 16.9910823292° = 16°59'27″ = 0.29765458091 rad
Angle ∠ C = γ = 20.7722254682° = 20°46'20″ = 0.36325442373 rad

Height: ha = 3.05108510792
Height: hb = 6.39436201309
Height: hc = 5.26880445687

Median: ma = 3.20215621187
Median: mb = 14.08990028036
Median: mc = 13.12444047484

Inradius: r = 1.484366399
Circumradius: R = 14.71989931833

Vertex coordinates: A[3; 5] B[6; -5] C[-4; 10]
Centroid: CG[1.66766666667; 3.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[4.85656276038; 1.484366399]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 37.7633077974° = 37°45'47″ = 2.48325026073 rad
∠ B' = β' = 163.0099176708° = 163°33″ = 0.29765458091 rad
∠ C' = γ' = 159.2287745318° = 159°13'40″ = 0.36325442373 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{ (6-(-4))**2 + (-5-10)**2 } ; ; a = sqrt{ 325 } = 18.03 ; ;

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{ (3-(-4))**2 + (5-10)**2 } ; ; b = sqrt{ 74 } = 8.6 ; ;

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{ (3-6)**2 + (5-(-5))**2 } ; ; c = sqrt{ 109 } = 10.44 ; ;


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 = 18.03 ; ; b = 8.6 ; ; c = 10.44 ; ;

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

p = a+b+c = 18.03+8.6+10.44 = 37.07 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37.07 }{ 2 } = 18.54 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.54 * (18.54-18.03)(18.54-8.6)(18.54-10.44) } ; ; T = sqrt{ 756.25 } = 27.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 27.5 }{ 18.03 } = 3.05 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 27.5 }{ 8.6 } = 6.39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 27.5 }{ 10.44 } = 5.27 ; ;

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{ 18.03**2-8.6**2-10.44**2 }{ 2 * 8.6 * 10.44 } ) = 142° 14'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8.6**2-18.03**2-10.44**2 }{ 2 * 18.03 * 10.44 } ) = 16° 59'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10.44**2-18.03**2-8.6**2 }{ 2 * 8.6 * 18.03 } ) = 20° 46'20" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 27.5 }{ 18.54 } = 1.48 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18.03 }{ 2 * sin 142° 14'13" } = 14.72 ; ;




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