Triangle calculator

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

You have entered side a, b and c.

Obtuse isosceles triangle.

Sides: a = 1000   b = 1423   c = 1000

Area: T = 499961.1587551
Perimeter: p = 3423
Semiperimeter: s = 1711.5

Angle ∠ A = α = 44.64329091312° = 44°38'34″ = 0.7799165752 rad
Angle ∠ B = β = 90.71441817375° = 90°42'51″ = 1.58332611496 rad
Angle ∠ C = γ = 44.64329091312° = 44°38'34″ = 0.7799165752 rad

Height: ha = 999.9222315102
Height: hb = 702.6866096347
Height: hc = 999.9222315102

Median: ma = 1123.594445531
Median: mb = 702.6866096347
Median: mc = 1123.594445531

Inradius: r = 292.1198701461
Circumradius: R = 711.5555277099

Vertex coordinates: A[1000; 0] B[0; 0] C[-12.46545; 999.9222315102]
Centroid: CG[329.17985; 333.3077438368]
Coordinates of the circumscribed circle: U[500; 506.2721579656]
Coordinates of the inscribed circle: I[288.5; 292.1198701461]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.3577090869° = 135°21'26″ = 0.7799165752 rad
∠ B' = β' = 89.28658182625° = 89°17'9″ = 1.58332611496 rad
∠ C' = γ' = 135.3577090869° = 135°21'26″ = 0.7799165752 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 = 1000 ; ; b = 1423 ; ; c = 1000 ; ;

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

p = a+b+c = 1000+1423+1000 = 3423 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 3423 }{ 2 } = 1711.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1711.5 * (1711.5-1000)(1711.5-1423)(1711.5-1000) } ; ; T = sqrt{ 249961159060 } = 499961.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 499961.16 }{ 1000 } = 999.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 499961.16 }{ 1423 } = 702.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 499961.16 }{ 1000 } = 999.92 ; ;

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{ 1000**2-1423**2-1000**2 }{ 2 * 1423 * 1000 } ) = 44° 38'34" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1423**2-1000**2-1000**2 }{ 2 * 1000 * 1000 } ) = 90° 42'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1000**2-1000**2-1423**2 }{ 2 * 1423 * 1000 } ) = 44° 38'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 499961.16 }{ 1711.5 } = 292.12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1000 }{ 2 * sin 44° 38'34" } = 711.56 ; ;




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