Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 14.31878210633   b = 7.07110678119   c = 18.02877563773

Area: T = 47.5
Perimeter: p = 39.41766452525
Semiperimeter: s = 19.70883226262

Angle ∠ A = α = 48.18798301199° = 48°10'47″ = 0.84108966686 rad
Angle ∠ B = β = 21.5955310449° = 21°35'43″ = 0.37769092703 rad
Angle ∠ C = γ = 110.2254859431° = 110°13'29″ = 1.92437867146 rad

Height: ha = 6.63550878098
Height: hb = 13.43550288425
Height: hc = 5.27696518641

Median: ma = 11.67326175299
Median: mb = 15.89902485821
Median: mc = 6.80107352544

Inradius: r = 2.41101493009
Circumradius: R = 9.60661643413

Vertex coordinates: A[7; 0] B[-8; 10] C[6; 7]
Centroid: CG[1.66766666667; 5.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[6.08987982339; 2.41101493009]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.822016988° = 131°49'13″ = 0.84108966686 rad
∠ B' = β' = 158.4054689551° = 158°24'17″ = 0.37769092703 rad
∠ C' = γ' = 69.77551405688° = 69°46'31″ = 1.92437867146 rad

Calculate another triangle


How did we calculate this triangle?

1. We compute side a from coordinates using the Pythagorean theorem

a = |BC| = |B-C| ; ; a**2 = (B_x-C_x)**2 + (B_y-C_y)**2 ; ; a = sqrt{ (B_x-C_x)**2 + (B_y-C_y)**2 } ; ; a = sqrt{ (-8-6)**2 + (10-7)**2 } ; ; a = sqrt{ 205 } = 14.32 ; ;

2. We compute side b from coordinates using the Pythagorean theorem

b = |AC| = |A-C| ; ; b**2 = (A_x-C_x)**2 + (A_y-C_y)**2 ; ; b = sqrt{ (A_x-C_x)**2 + (A_y-C_y)**2 } ; ; b = sqrt{ (7-6)**2 + (0-7)**2 } ; ; b = sqrt{ 50 } = 7.07 ; ;

3. We compute side c from coordinates using the Pythagorean theorem

c = |AB| = |A-B| ; ; c**2 = (A_x-B_x)**2 + (A_y-B_y)**2 ; ; c = sqrt{ (A_x-B_x)**2 + (A_y-B_y)**2 } ; ; c = sqrt{ (7-(-8))**2 + (0-10)**2 } ; ; c = sqrt{ 325 } = 18.03 ; ;
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 = 14.32 ; ; b = 7.07 ; ; c = 18.03 ; ;

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

p = a+b+c = 14.32+7.07+18.03 = 39.42 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39.42 }{ 2 } = 19.71 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.71 * (19.71-14.32)(19.71-7.07)(19.71-18.03) } ; ; T = sqrt{ 2256.25 } = 47.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.5 }{ 14.32 } = 6.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.5 }{ 7.07 } = 13.44 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.5 }{ 18.03 } = 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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 7.07**2+18.03**2-14.32**2 }{ 2 * 7.07 * 18.03 } ) = 48° 10'47" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14.32**2+18.03**2-7.07**2 }{ 2 * 14.32 * 18.03 } ) = 21° 35'43" ; ;
 gamma = 180° - alpha - beta = 180° - 48° 10'47" - 21° 35'43" = 110° 13'29" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.5 }{ 19.71 } = 2.41 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14.32 }{ 2 * sin 48° 10'47" } = 9.61 ; ;

11. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.07**2+2 * 18.03**2 - 14.32**2 } }{ 2 } = 11.673 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 18.03**2+2 * 14.32**2 - 7.07**2 } }{ 2 } = 15.89 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.07**2+2 * 14.32**2 - 18.03**2 } }{ 2 } = 6.801 ; ;
Calculate another triangle


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

See more information about triangles or more details on solving triangles.