Triangle calculator

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

You have entered side a, c and angle β.

Acute isosceles triangle.

Sides: a = 5.5   b = 2.38108357533   c = 5.5

Area: T = 6.39221012088
Perimeter: p = 13.38108357533
Semiperimeter: s = 6.69904178767

Angle ∠ A = α = 77.5° = 77°30' = 1.35326301703 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 77.5° = 77°30' = 1.35326301703 rad

Height: ha = 2.32444004396
Height: hb = 5.37696280392
Height: hc = 2.32444004396

Median: ma = 3.22443897783
Median: mb = 5.37696280392
Median: mc = 3.22443897783

Inradius: r = 0.9555411355
Circumradius: R = 2.81767686644

Vertex coordinates: A[5.5; 0] B[0; 0] C[4.98546928287; 2.32444004396]
Centroid: CG[3.49548976096; 0.77548001465]
Coordinates of the circumscribed circle: U[2.75; 0.61096603223]
Coordinates of the inscribed circle: I[4.31095821233; 0.9555411355]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 102.5° = 102°30' = 1.35326301703 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 102.5° = 102°30' = 1.35326301703 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 = 2.38 ; ; c = 5.5 ; ;

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

p = a+b+c = 5.5+2.38+5.5 = 13.38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13.38 }{ 2 } = 6.69 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.69 * (6.69-5.5)(6.69-2.38)(6.69-5.5) } ; ; T = sqrt{ 40.86 } = 6.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6.39 }{ 5.5 } = 2.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6.39 }{ 2.38 } = 5.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6.39 }{ 5.5 } = 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**2-2.38**2-5.5**2 }{ 2 * 2.38 * 5.5 } ) = 77° 30' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2.38**2-5.5**2-5.5**2 }{ 2 * 5.5 * 5.5 } ) = 25° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.5**2-5.5**2-2.38**2 }{ 2 * 2.38 * 5.5 } ) = 77° 30' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6.39 }{ 6.69 } = 0.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5.5 }{ 2 * sin 77° 30' } = 2.82 ; ;




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