Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 25.96215099715   b = 43.68106593357   c = 17.72200451467

Area: T = 3
Perimeter: p = 87.36222144538
Semiperimeter: s = 43.68111072269

Angle ∠ A = α = 0.44441444331° = 0°26'39″ = 0.00877517827 rad
Angle ∠ B = β = 179.2532706123° = 179°15'10″ = 3.1298549915 rad
Angle ∠ C = γ = 0.30331494437° = 0°18'11″ = 0.00552909559 rad

Height: ha = 0.23111113647
Height: hb = 0.13773605639
Height: hc = 0.33985995888

Median: ma = 30.7700162866
Median: mb = 4.12331056256
Median: mc = 34.8210970693

Inradius: r = 0.06986795778
Circumradius: R = 1674.568770541

Vertex coordinates: A[-5; 3] B[12; 8] C[37; 15]
Centroid: CG[14.66766666667; 8.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[-5.26554342942; 0.06986795778]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 179.5565855567° = 179°33'21″ = 0.00877517827 rad
∠ B' = β' = 0.74772938768° = 0°44'50″ = 3.1298549915 rad
∠ C' = γ' = 179.6976850556° = 179°41'49″ = 0.00552909559 rad

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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{ (12-37)**2 + (8-15)**2 } ; ; a = sqrt{ 674 } = 25.96 ; ;

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{ (-5-37)**2 + (3-15)**2 } ; ; b = sqrt{ 1908 } = 43.68 ; ;

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{ (-5-12)**2 + (3-8)**2 } ; ; c = sqrt{ 314 } = 17.72 ; ;


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 = 25.96 ; ; b = 43.68 ; ; c = 17.72 ; ;

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

p = a+b+c = 25.96+43.68+17.72 = 87.36 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 87.36 }{ 2 } = 43.68 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 43.68 * (43.68-25.96)(43.68-43.68)(43.68-17.72) } ; ; T = sqrt{ 9 } = 3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3 }{ 25.96 } = 0.23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3 }{ 43.68 } = 0.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3 }{ 17.72 } = 0.34 ; ;

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{ 43.68**2+17.72**2-25.96**2 }{ 2 * 43.68 * 17.72 } ) = 0° 26'39" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 25.96**2+17.72**2-43.68**2 }{ 2 * 25.96 * 17.72 } ) = 179° 15'10" ; ; gamma = 180° - alpha - beta = 180° - 0° 26'39" - 179° 15'10" = 0° 18'11" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3 }{ 43.68 } = 0.07 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 25.96 }{ 2 * sin 0° 26'39" } = 1674.57 ; ;

11. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 43.68**2+2 * 17.72**2 - 25.96**2 } }{ 2 } = 30.7 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 17.72**2+2 * 25.96**2 - 43.68**2 } }{ 2 } = 4.123 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 43.68**2+2 * 25.96**2 - 17.72**2 } }{ 2 } = 34.821 ; ;
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