Isosceles triangle calculator (A,c)

Please enter two properties of the isosceles triangle

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


You have entered side c and angle α.

Right isosceles triangle.

Sides: a = 63.64396103068   b = 63.64396103068   c = 90

Area: T = 2025
Perimeter: p = 217.2799220614
Semiperimeter: s = 108.6439610307

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 63.64396103068
Height: hb = 63.64396103068
Height: hc = 45

Median: ma = 71.15112473538
Median: mb = 71.15112473538
Median: mc = 45

Inradius: r = 18.64396103068
Circumradius: R = 45

Vertex coordinates: A[90; 0] B[0; 0] C[45; 45]
Centroid: CG[45; 15]
Coordinates of the circumscribed circle: U[45; -0]
Coordinates of the inscribed circle: I[45; 18.64396103068]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 135° = 0.78553981634 rad
∠ C' = γ' = 90° = 1.57107963268 rad

Calculate another triangle




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 = 63.64 ; ; b = 63.64 ; ; c = 90 ; ;

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

p = a+b+c = 63.64+63.64+90 = 217.28 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 217.28 }{ 2 } = 108.64 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 108.64 * (108.64-63.64)(108.64-63.64)(108.64-90) } ; ; T = sqrt{ 4100625 } = 2025 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2025 }{ 63.64 } = 63.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2025 }{ 63.64 } = 63.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2025 }{ 90 } = 45 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 63.64**2+90**2-63.64**2 }{ 2 * 63.64 * 90 } ) = 45° ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 63.64**2+90**2-63.64**2 }{ 2 * 63.64 * 90 } ) = 45° ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 63.64**2+63.64**2-90**2 }{ 2 * 63.64 * 63.64 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2025 }{ 108.64 } = 18.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 63.64 }{ 2 * sin 45° } = 45 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 63.64**2+2 * 90**2 - 63.64**2 } }{ 2 } = 71.151 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 63.64**2 - 63.64**2 } }{ 2 } = 71.151 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 63.64**2+2 * 63.64**2 - 90**2 } }{ 2 } = 45 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.