Triangle calculator VC

Please enter the coordinates of the three vertices


Acute scalene triangle.

Sides: a = 7.07110678119   b = 10.81766538264   c = 11.70546999107

Area: T = 37.5
Perimeter: p = 29.5922421549
Semiperimeter: s = 14.79662107745

Angle ∠ A = α = 36.32768259521° = 36°19'37″ = 0.63440227197 rad
Angle ∠ B = β = 64.98331065219° = 64°58'59″ = 1.1344169167 rad
Angle ∠ C = γ = 78.6990067526° = 78°41'24″ = 1.37334007669 rad

Height: ha = 10.60766017178
Height: hb = 6.93437524528
Height: hc = 6.40876824329

Median: ma = 10.77004672795
Median: mb = 8.01656097709
Median: mc = 7.01878344238

Inradius: r = 2.53444326714
Circumradius: R = 5.96882493246

Vertex coordinates: A[-5; 8] B[-1; -3] C[4; 2]
Centroid: CG[-0.66766666667; 2.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.18327352467; 2.53444326714]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.6733174048° = 143°40'23″ = 0.63440227197 rad
∠ B' = β' = 115.0176893478° = 115°1'1″ = 1.1344169167 rad
∠ C' = γ' = 101.3109932474° = 101°18'36″ = 1.37334007669 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{ (-1-4)**2 + (-3-2)**2 } ; ; a = sqrt{ 50 } = 7.07 ; ;

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{ (-5-4)**2 + (8-2)**2 } ; ; b = sqrt{ 117 } = 10.82 ; ;

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{ (-5-(-1))**2 + (8-(-3))**2 } ; ; c = sqrt{ 137 } = 11.7 ; ;


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 = 7.07 ; ; b = 10.82 ; ; c = 11.7 ; ;

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

p = a+b+c = 7.07+10.82+11.7 = 29.59 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29.59 }{ 2 } = 14.8 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.8 * (14.8-7.07)(14.8-10.82)(14.8-11.7) } ; ; T = sqrt{ 1406.25 } = 37.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 37.5 }{ 7.07 } = 10.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 37.5 }{ 10.82 } = 6.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 37.5 }{ 11.7 } = 6.41 ; ;

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{ 7.07**2-10.82**2-11.7**2 }{ 2 * 10.82 * 11.7 } ) = 36° 19'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10.82**2-7.07**2-11.7**2 }{ 2 * 7.07 * 11.7 } ) = 64° 58'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11.7**2-7.07**2-10.82**2 }{ 2 * 10.82 * 7.07 } ) = 78° 41'24" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 37.5 }{ 14.8 } = 2.53 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7.07 }{ 2 * sin 36° 19'37" } = 5.97 ; ;




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