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 = 137.091   b = 137.091   c = 102.818

Area: T = 6533.406575947
Perimeter: p = 377
Semiperimeter: s = 188.5

Angle ∠ A = α = 67.97657435179° = 67°58'33″ = 1.18664005359 rad
Angle ∠ B = β = 67.97657435179° = 67°58'33″ = 1.18664005359 rad
Angle ∠ C = γ = 44.04985129641° = 44°2'55″ = 0.76987915818 rad

Height: ha = 95.31548749294
Height: hb = 95.31548749294
Height: hc = 127.0876808914

Median: ma = 99.92112496532
Median: mb = 99.92112496532
Median: mc = 127.0876808914

Inradius: r = 34.66599775038
Circumradius: R = 73.94113572564

Vertex coordinates: A[102.818; 0] B[0; 0] C[51.409; 127.0876808914]
Centroid: CG[51.409; 42.36222696381]
Coordinates of the circumscribed circle: U[51.409; 53.14554516578]
Coordinates of the inscribed circle: I[51.409; 34.66599775038]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.0244256482° = 112°1'27″ = 1.18664005359 rad
∠ B' = β' = 112.0244256482° = 112°1'27″ = 1.18664005359 rad
∠ C' = γ' = 135.9511487036° = 135°57'5″ = 0.76987915818 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 = 137.09 ; ; b = 137.09 ; ; c = 102.82 ; ;

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

p = a+b+c = 137.09+137.09+102.82 = 377 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 377 }{ 2 } = 188.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 188.5 * (188.5-137.09)(188.5-137.09)(188.5-102.82) } ; ; T = sqrt{ 42685390.82 } = 6533.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6533.41 }{ 137.09 } = 95.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6533.41 }{ 137.09 } = 95.31 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6533.41 }{ 102.82 } = 127.09 ; ;

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{ 137.09**2-137.09**2-102.82**2 }{ 2 * 137.09 * 102.82 } ) = 67° 58'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 137.09**2-137.09**2-102.82**2 }{ 2 * 137.09 * 102.82 } ) = 67° 58'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 102.82**2-137.09**2-137.09**2 }{ 2 * 137.09 * 137.09 } ) = 44° 2'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6533.41 }{ 188.5 } = 34.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 137.09 }{ 2 * sin 67° 58'33" } = 73.94 ; ;




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