Right triangle calculator (a,b)

Please enter two properties of the right triangle

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


You have entered cathetus a and cathetus b.

Right isosceles triangle.

Sides: a = 62.83   b = 62.83   c = 88.85550381239

Area: T = 1973.804445
Perimeter: p = 214.5155038124
Semiperimeter: s = 107.2587519062

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

Height: ha = 62.83
Height: hb = 62.83
Height: hc = 44.4287519062

Median: ma = 70.24660755132
Median: mb = 70.24660755132
Median: mc = 44.4287519062

Inradius: r = 18.4022480938
Circumradius: R = 44.4287519062

Vertex coordinates: A[88.85550381239; 0] B[0; 0] C[44.4287519062; 44.4287519062]
Centroid: CG[44.4287519062; 14.80991730207]
Coordinates of the circumscribed circle: U[44.4287519062; 0]
Coordinates of the inscribed circle: I[44.4287519062; 18.4022480938]

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?

1. Input data entered: cathetus a cathetus b

a = 62.83 ; ; b = 62.83 ; ;

2. From cathetus a and cathetus b we calculate hypotenuse c - Pythagorean theorem:

c**2 = a**2+b**2 ; ; c = sqrt{ a**2+b**2 } = sqrt{ 62.83**2 + 62.83**2 } = 88.855 ; ;


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 = 62.83 ; ; b = 62.83 ; ; c = 88.86 ; ;

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

p = a+b+c = 62.83+62.83+88.86 = 214.52 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 214.52 }{ 2 } = 107.26 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 107.26 * (107.26-62.83)(107.26-62.83)(107.26-88.86) } ; ; T = sqrt{ 3895904.01 } = 1973.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1973.8 }{ 62.83 } = 62.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1973.8 }{ 62.83 } = 62.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1973.8 }{ 88.86 } = 44.43 ; ;

7. 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{ 62.83**2-62.83**2-88.86**2 }{ 2 * 62.83 * 88.86 } ) = 45° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 62.83**2-62.83**2-88.86**2 }{ 2 * 62.83 * 88.86 } ) = 45° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 88.86**2-62.83**2-62.83**2 }{ 2 * 62.83 * 62.83 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1973.8 }{ 107.26 } = 18.4 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 62.83 }{ 2 * sin 45° } = 44.43 ; ;
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