Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and c.

Acute isosceles triangle.

Sides: a = 443   b = 443   c = 610

Area: T = 97991.90106857
Perimeter: p = 1496
Semiperimeter: s = 748

Angle ∠ A = α = 46.4899492991° = 46°29'22″ = 0.81113947203 rad
Angle ∠ B = β = 46.4899492991° = 46°29'22″ = 0.81113947203 rad
Angle ∠ C = γ = 87.0211014018° = 87°1'16″ = 1.5198803213 rad

Height: ha = 442.4011357498
Height: hb = 442.4011357498
Height: hc = 321.2854920281

Median: ma = 484.8843748954
Median: mb = 484.8843748954
Median: mc = 321.2854920281

Inradius: r = 131.005521482
Circumradius: R = 305.4132715649

Vertex coordinates: A[610; 0] B[0; 0] C[305; 321.2854920281]
Centroid: CG[305; 107.0954973427]
Coordinates of the circumscribed circle: U[305; 15.87222046324]
Coordinates of the inscribed circle: I[305; 131.005521482]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.5110507009° = 133°30'38″ = 0.81113947203 rad
∠ B' = β' = 133.5110507009° = 133°30'38″ = 0.81113947203 rad
∠ C' = γ' = 92.9798985982° = 92°58'44″ = 1.5198803213 rad

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How did we calculate this triangle?

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 = 443 ; ; b = 443 ; ; c = 610 ; ;

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

p = a+b+c = 443+443+610 = 1496 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1496 }{ 2 } = 748 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 748 * (748-443)(748-443)(748-610) } ; ; T = sqrt{ 9602412600 } = 97991.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 97991.9 }{ 443 } = 442.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 97991.9 }{ 443 } = 442.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 97991.9 }{ 610 } = 321.28 ; ;

5. 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{ 443**2-443**2-610**2 }{ 2 * 443 * 610 } ) = 46° 29'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 443**2-443**2-610**2 }{ 2 * 443 * 610 } ) = 46° 29'22" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 610**2-443**2-443**2 }{ 2 * 443 * 443 } ) = 87° 1'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 97991.9 }{ 748 } = 131.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 443 }{ 2 * sin 46° 29'22" } = 305.41 ; ;




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