Isosceles triangle calculator (h)

Please enter two properties of the isosceles triangle

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


You have entered height hc and angle γ.

Acute isosceles triangle.

Sides: a = 502.708822243   b = 502.708822243   c = 104.2222011095

Area: T = 26055.50327737
Perimeter: p = 1109.638845596
Semiperimeter: s = 554.8199227978

Angle ∠ A = α = 84.05° = 84°3' = 1.46769492363 rad
Angle ∠ B = β = 84.05° = 84°3' = 1.46769492363 rad
Angle ∠ C = γ = 11.9° = 11°54' = 0.2087694181 rad

Height: ha = 103.6610539499
Height: hb = 103.6610539499
Height: hc = 500

Median: ma = 261.9355112238
Median: mb = 261.9355112238
Median: mc = 500

Inradius: r = 46.96221481373
Circumradius: R = 252.7165556899

Vertex coordinates: A[104.2222011095; 0] B[0; 0] C[52.11110055474; 500]
Centroid: CG[52.11110055474; 166.6676666667]
Coordinates of the circumscribed circle: U[52.11110055474; 247.2844443101]
Coordinates of the inscribed circle: I[52.11110055474; 46.96221481373]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 95.95° = 95°57' = 1.46769492363 rad
∠ B' = β' = 95.95° = 95°57' = 1.46769492363 rad
∠ C' = γ' = 168.1° = 168°6' = 0.2087694181 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 = 502.71 ; ; b = 502.71 ; ; c = 104.22 ; ;

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

p = a+b+c = 502.71+502.71+104.22 = 1109.64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1109.64 }{ 2 } = 554.82 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 554.82 * (554.82-502.71)(554.82-502.71)(554.82-104.22) } ; ; T = sqrt{ 678889224.79 } = 26055.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26055.5 }{ 502.71 } = 103.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26055.5 }{ 502.71 } = 103.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26055.5 }{ 104.22 } = 500 ; ;

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{ 502.71**2-502.71**2-104.22**2 }{ 2 * 502.71 * 104.22 } ) = 84° 3' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 502.71**2-502.71**2-104.22**2 }{ 2 * 502.71 * 104.22 } ) = 84° 3' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 104.22**2-502.71**2-502.71**2 }{ 2 * 502.71 * 502.71 } ) = 11° 54' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26055.5 }{ 554.82 } = 46.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 502.71 }{ 2 * sin 84° 3' } = 252.72 ; ;




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