Triangle calculator

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

You have entered side a, area S and angle β.

Obtuse scalene triangle.

Sides: a = 5.5   b = 5.82444584676   c = 10.32552432719

Area: T = 12
Perimeter: p = 21.65497017395
Semiperimeter: s = 10.82548508697

Angle ∠ A = α = 23.52204151622° = 23°31'14″ = 0.4110508686 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 131.4879584838° = 131°28'46″ = 2.29547516546 rad

Height: ha = 4.36436363636
Height: hb = 4.12105547492
Height: hc = 2.32444004396

Median: ma = 7.91986477717
Median: mb = 7.74326897912
Median: mc = 2.33112005628

Inradius: r = 1.10985603067
Circumradius: R = 6.89109214235

Vertex coordinates: A[10.32552432719; 0] B[0; 0] C[4.98546928287; 2.32444004396]
Centroid: CG[5.10333120335; 0.77548001465]
Coordinates of the circumscribed circle: U[5.1632621636; -4.56442234726]
Coordinates of the inscribed circle: I[55.0003924022; 1.10985603067]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.4879584838° = 156°28'46″ = 0.4110508686 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 48.52204151622° = 48°31'14″ = 2.29547516546 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 = 5.5 ; ; b = 5.82 ; ; c = 10.33 ; ;

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

p = a+b+c = 5.5+5.82+10.33 = 21.65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 21.65 }{ 2 } = 10.82 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.82 * (10.82-5.5)(10.82-5.82)(10.82-10.33) } ; ; T = sqrt{ 144 } = 12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12 }{ 5.5 } = 4.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12 }{ 5.82 } = 4.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12 }{ 10.33 } = 2.32 ; ;

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{ 5.5**2-5.82**2-10.33**2 }{ 2 * 5.82 * 10.33 } ) = 23° 31'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.82**2-5.5**2-10.33**2 }{ 2 * 5.5 * 10.33 } ) = 25° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10.33**2-5.5**2-5.82**2 }{ 2 * 5.82 * 5.5 } ) = 131° 28'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12 }{ 10.82 } = 1.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5.5 }{ 2 * sin 23° 31'14" } = 6.89 ; ;




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