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 = 10.25112626585   b = 10.25112626585   c = 14.49774746831

Area: T = 52.54441930465
Perimeter: p = 35
Semiperimeter: s = 17.5

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

Height: ha = 10.25112626585
Height: hb = 10.25112626585
Height: hc = 7.24987373415

Median: ma = 11.46112600798
Median: mb = 11.46112600798
Median: mc = 7.24987373415

Inradius: r = 3.00325253169
Circumradius: R = 7.24987373415

Vertex coordinates: A[14.49774746831; 0] B[0; 0] C[7.24987373415; 7.24987373415]
Centroid: CG[7.24987373415; 2.41662457805]
Coordinates of the circumscribed circle: U[7.24987373415; 0]
Coordinates of the inscribed circle: I[7.24987373415; 3.00325253169]

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 = 10.25 ; ; b = 10.25 ; ; c = 14.5 ; ;

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

p = a+b+c = 10.25+10.25+14.5 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-10.25)(17.5-10.25)(17.5-14.5) } ; ; T = sqrt{ 2760.89 } = 52.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 52.54 }{ 10.25 } = 10.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 52.54 }{ 10.25 } = 10.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 52.54 }{ 14.5 } = 7.25 ; ;

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{ 10.25**2-10.25**2-14.5**2 }{ 2 * 10.25 * 14.5 } ) = 45° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10.25**2-10.25**2-14.5**2 }{ 2 * 10.25 * 14.5 } ) = 45° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14.5**2-10.25**2-10.25**2 }{ 2 * 10.25 * 10.25 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 52.54 }{ 17.5 } = 3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10.25 }{ 2 * sin 45° } = 7.25 ; ;




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