Isosceles triangle calculator (S)

Please enter two properties of the isosceles triangle

Use symbols: a, b, h, T, p, A, B, C, r, R


You have entered area S and perimeter p.

Obtuse isosceles triangle.

Sides: a = 6.4055053919   b = 6.4055053919   c = 12.19898921621

Area: T = 12
Perimeter: p = 25
Semiperimeter: s = 12.5

Angle ∠ A = α = 17.90219610843° = 17°54'7″ = 0.31224481635 rad
Angle ∠ B = β = 17.90219610843° = 17°54'7″ = 0.31224481635 rad
Angle ∠ C = γ = 144.1966077831° = 144°11'46″ = 2.51766963266 rad

Height: ha = 3.7477041056
Height: hb = 3.7477041056
Height: hc = 1.96988443245

Median: ma = 9.19552658682
Median: mb = 9.19552658682
Median: mc = 1.96988443245

Inradius: r = 0.96
Circumradius: R = 10.41884762588

Vertex coordinates: A[12.19898921621; 0] B[0; 0] C[6.0954946081; 1.96988443245]
Centroid: CG[6.0954946081; 0.65662814415]
Coordinates of the circumscribed circle: U[6.0954946081; -8.45496319343]
Coordinates of the inscribed circle: I[6.0954946081; 0.96]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.0988038916° = 162°5'53″ = 0.31224481635 rad
∠ B' = β' = 162.0988038916° = 162°5'53″ = 0.31224481635 rad
∠ C' = γ' = 35.80439221686° = 35°48'14″ = 2.51766963266 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 = 6.41 ; ; b = 6.41 ; ; c = 12.19 ; ;

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

p = a+b+c = 6.41+6.41+12.19 = 25 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 25 }{ 2 } = 12.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.5 * (12.5-6.41)(12.5-6.41)(12.5-12.19) } ; ; 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 }{ 6.41 } = 3.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12 }{ 6.41 } = 3.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12 }{ 12.19 } = 1.97 ; ;

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{ 6.41**2-6.41**2-12.19**2 }{ 2 * 6.41 * 12.19 } ) = 17° 54'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6.41**2-6.41**2-12.19**2 }{ 2 * 6.41 * 12.19 } ) = 17° 54'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12.19**2-6.41**2-6.41**2 }{ 2 * 6.41 * 6.41 } ) = 144° 11'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12 }{ 12.5 } = 0.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.41 }{ 2 * sin 17° 54'7" } = 10.42 ; ;




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