Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 8.24662112512   b = 14.56602197786   c = 6.32545553203

Area: T = 2
Perimeter: p = 29.13109863501
Semiperimeter: s = 14.56554931751

Angle ∠ A = α = 2.4989552922° = 2°29'22″ = 0.04334508954 rad
Angle ∠ B = β = 175.6011294645° = 175°36'5″ = 3.06548207623 rad
Angle ∠ C = γ = 1.9099152433° = 1°54'33″ = 0.03333209959 rad

Height: ha = 0.48550712501
Height: hb = 0.27547211279
Height: hc = 0.6322455532

Median: ma = 10.44403065089
Median: mb = 1
Median: mc = 11.4021754251

Inradius: r = 0.13773108329
Circumradius: R = 94.92110198007

Vertex coordinates: A[-5; 4] B[1; 2] C[9; 0]
Centroid: CG[1.66766666667; 2]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[-1.78550408282; 0.13773108329]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 177.5110447078° = 177°30'38″ = 0.04334508954 rad
∠ B' = β' = 4.3998705355° = 4°23'55″ = 3.06548207623 rad
∠ C' = γ' = 178.0910847567° = 178°5'27″ = 0.03333209959 rad

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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{ (1-9)**2 + (2-0)**2 } ; ; a = sqrt{ 68 } = 8.25 ; ;

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{ (-5-9)**2 + (4-0)**2 } ; ; b = sqrt{ 212 } = 14.56 ; ;

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 + (4-2)**2 } ; ; c = sqrt{ 40 } = 6.32 ; ;


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 = 8.25 ; ; b = 14.56 ; ; c = 6.32 ; ;

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

p = a+b+c = 8.25+14.56+6.32 = 29.13 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29.13 }{ 2 } = 14.57 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.57 * (14.57-8.25)(14.57-14.56)(14.57-6.32) } ; ; T = sqrt{ 4 } = 2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2 }{ 8.25 } = 0.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2 }{ 14.56 } = 0.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2 }{ 6.32 } = 0.63 ; ;

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{ 8.25**2-14.56**2-6.32**2 }{ 2 * 14.56 * 6.32 } ) = 2° 29'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14.56**2-8.25**2-6.32**2 }{ 2 * 8.25 * 6.32 } ) = 175° 36'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.32**2-8.25**2-14.56**2 }{ 2 * 14.56 * 8.25 } ) = 1° 54'33" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2 }{ 14.57 } = 0.14 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8.25 }{ 2 * sin 2° 29'22" } = 94.92 ; ;




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