Isosceles triangle calculator (p)

Please enter two properties of the isosceles triangle

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


You have entered perimeter p and angle γ.

Right isosceles triangle.

Sides: a = 116.8644394307   b = 116.8644394307   c = 165.2711211387

Area: T = 6828.643332832
Perimeter: p = 399
Semiperimeter: s = 199.5

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

Height: ha = 116.8644394307
Height: hb = 116.8644394307
Height: hc = 82.63656056934

Median: ma = 130.6588364909
Median: mb = 130.6588364909
Median: mc = 82.63656056934

Inradius: r = 34.22987886131
Circumradius: R = 82.63656056934

Vertex coordinates: A[165.2711211387; 0] B[0; 0] C[82.63656056934; 82.63656056934]
Centroid: CG[82.63656056934; 27.54552018978]
Coordinates of the circumscribed circle: U[82.63656056934; 0]
Coordinates of the inscribed circle: I[82.63656056934; 34.22987886131]

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

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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 = 116.86 ; ; b = 116.86 ; ; c = 165.27 ; ;

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

p = a+b+c = 116.86+116.86+165.27 = 399 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 399 }{ 2 } = 199.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 199.5 * (199.5-116.86)(199.5-116.86)(199.5-165.27) } ; ; T = sqrt{ 46630369.71 } = 6828.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6828.64 }{ 116.86 } = 116.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6828.64 }{ 116.86 } = 116.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6828.64 }{ 165.27 } = 82.64 ; ;

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{ 116.86**2-116.86**2-165.27**2 }{ 2 * 116.86 * 165.27 } ) = 45° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 116.86**2-116.86**2-165.27**2 }{ 2 * 116.86 * 165.27 } ) = 45° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 165.27**2-116.86**2-116.86**2 }{ 2 * 116.86 * 116.86 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6828.64 }{ 199.5 } = 34.23 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 116.86 }{ 2 * sin 45° } = 82.64 ; ;




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