Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and c (hypotenuse-calculated).

Right isosceles triangle.

Sides: a = 60.75   b = 60.75   c = 85.91334739142

Area: T = 1845.281125
Perimeter: p = 207.4133473914
Semiperimeter: s = 103.7076736957

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

Height: ha = 60.75
Height: hb = 60.75
Height: hc = 42.95767369571

Median: ma = 67.92105648166
Median: mb = 67.92105648166
Median: mc = 42.95767369571

Inradius: r = 17.79332630429
Circumradius: R = 42.95767369571

Vertex coordinates: A[85.91334739142; 0] B[0; 0] C[42.95767369571; 42.95767369571]
Centroid: CG[42.95767369571; 14.3198912319]
Coordinates of the circumscribed circle: U[42.95767369571; -0]
Coordinates of the inscribed circle: I[42.95767369571; 17.79332630429]

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: side a, b and c (hypotenuse-calculated).

a = 60.75 ; ; b = 60.75 ; ; c = 85.913 ; ;

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

p = a+b+c = 60.75+60.75+85.91 = 207.41 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 207.41 }{ 2 } = 103.71 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 103.71 * (103.71-60.75)(103.71-60.75)(103.71-85.91) } ; ; T = sqrt{ 3405062.89 } = 1845.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1845.28 }{ 60.75 } = 60.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1845.28 }{ 60.75 } = 60.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1845.28 }{ 85.91 } = 42.96 ; ;

6. 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{ 60.75**2+85.91**2-60.75**2 }{ 2 * 60.75 * 85.91 } ) = 45° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 60.75**2+85.91**2-60.75**2 }{ 2 * 60.75 * 85.91 } ) = 45° ; ; gamma = 180° - alpha - beta = 180° - 45° - 45° = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1845.28 }{ 103.71 } = 17.79 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 60.75 }{ 2 * sin 45° } = 42.96 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 60.75**2+2 * 85.91**2 - 60.75**2 } }{ 2 } = 67.921 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 85.91**2+2 * 60.75**2 - 60.75**2 } }{ 2 } = 67.921 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 60.75**2+2 * 60.75**2 - 85.91**2 } }{ 2 } = 42.957 ; ;
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