Isosceles triangle calculator (a,b)

Please enter two properties of the isosceles triangle

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


You have entered side a and b.

Acute isosceles triangle.

Sides: a = 112.727   b = 112.727   c = 84.545

Area: T = 4417.509907129
Perimeter: p = 309.999
Semiperimeter: s = 1554.9995

Angle ∠ A = α = 67.97657556981° = 67°58'33″ = 1.18664007485 rad
Angle ∠ B = β = 67.97657556981° = 67°58'33″ = 1.18664007485 rad
Angle ∠ C = γ = 44.04884886038° = 44°2'55″ = 0.76987911567 rad

Height: ha = 78.375535056
Height: hb = 78.375535056
Height: hc = 104.5010776422

Median: ma = 82.16330856574
Median: mb = 82.16330856574
Median: mc = 104.5010776422

Inradius: r = 28.55001504604
Circumradius: R = 60.88003928971

Vertex coordinates: A[84.545; 0] B[0; 0] C[42.27325; 104.5010776422]
Centroid: CG[42.27325; 34.83435921406]
Coordinates of the circumscribed circle: U[42.27325; 43.77003835246]
Coordinates of the inscribed circle: I[42.27325; 28.55001504604]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.0244244302° = 112°1'27″ = 1.18664007485 rad
∠ B' = β' = 112.0244244302° = 112°1'27″ = 1.18664007485 rad
∠ C' = γ' = 135.9521511396° = 135°57'5″ = 0.76987911567 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 = 112.73 ; ; b = 112.73 ; ; c = 84.55 ; ;

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

p = a+b+c = 112.73+112.73+84.55 = 310 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 310 }{ 2 } = 155 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 155 * (155-112.73)(155-112.73)(155-84.55) } ; ; T = sqrt{ 19514386.39 } = 4417.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4417.51 }{ 112.73 } = 78.38 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4417.51 }{ 112.73 } = 78.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4417.51 }{ 84.55 } = 104.5 ; ;

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{ 112.73**2-112.73**2-84.55**2 }{ 2 * 112.73 * 84.55 } ) = 67° 58'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 112.73**2-112.73**2-84.55**2 }{ 2 * 112.73 * 84.55 } ) = 67° 58'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 84.55**2-112.73**2-112.73**2 }{ 2 * 112.73 * 112.73 } ) = 44° 2'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4417.51 }{ 155 } = 28.5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 112.73 }{ 2 * sin 67° 58'33" } = 60.8 ; ;




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