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 = 46.545   b = 46.545   c = 34.909

Area: T = 753.1322338481
Perimeter: p = 127.999
Semiperimeter: s = 643.9995

Angle ∠ A = α = 67.97655211781° = 67°58'32″ = 1.18663966553 rad
Angle ∠ B = β = 67.97655211781° = 67°58'32″ = 1.18663966553 rad
Angle ∠ C = γ = 44.04989576438° = 44°2'56″ = 0.7698799343 rad

Height: ha = 32.36114711991
Height: hb = 32.36114711991
Height: hc = 43.14883192575

Median: ma = 33.92553356174
Median: mb = 33.92553356174
Median: mc = 43.14883192575

Inradius: r = 11.76877847246
Circumradius: R = 25.10545354985

Vertex coordinates: A[34.909; 0] B[0; 0] C[17.45545; 43.14883192575]
Centroid: CG[17.45545; 14.38327730858]
Coordinates of the circumscribed circle: U[17.45545; 18.04437837591]
Coordinates of the inscribed circle: I[17.45545; 11.76877847246]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.0244478822° = 112°1'28″ = 1.18663966553 rad
∠ B' = β' = 112.0244478822° = 112°1'28″ = 1.18663966553 rad
∠ C' = γ' = 135.9511042356° = 135°57'4″ = 0.7698799343 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 = 46.55 ; ; b = 46.55 ; ; c = 34.91 ; ;

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

p = a+b+c = 46.55+46.55+34.91 = 128 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 128 }{ 2 } = 64 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 64 * (64-46.55)(64-46.55)(64-34.91) } ; ; T = sqrt{ 567208.32 } = 753.13 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 753.13 }{ 46.55 } = 32.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 753.13 }{ 46.55 } = 32.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 753.13 }{ 34.91 } = 43.15 ; ;

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{ 46.55**2-46.55**2-34.91**2 }{ 2 * 46.55 * 34.91 } ) = 67° 58'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 46.55**2-46.55**2-34.91**2 }{ 2 * 46.55 * 34.91 } ) = 67° 58'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 34.91**2-46.55**2-46.55**2 }{ 2 * 46.55 * 46.55 } ) = 44° 2'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 753.13 }{ 64 } = 11.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 46.55 }{ 2 * sin 67° 58'32" } = 25.1 ; ;




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