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 = 32   b = 32   c = 45.25548339959

Area: T = 512
Perimeter: p = 109.2554833996
Semiperimeter: s = 54.6277416998

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

Height: ha = 32
Height: hb = 32
Height: hc = 22.6277416998

Median: ma = 35.777708764
Median: mb = 35.777708764
Median: mc = 22.6277416998

Inradius: r = 9.3732583002
Circumradius: R = 22.6277416998

Vertex coordinates: A[45.25548339959; 0] B[0; 0] C[22.6277416998; 22.6277416998]
Centroid: CG[22.6277416998; 7.54224723327]
Coordinates of the circumscribed circle: U[22.6277416998; -0]
Coordinates of the inscribed circle: I[22.6277416998; 9.3732583002]

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 and cathetus b

a = 32 ; ; b = 32 ; ;

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{ 32**2 + 32**2 } = sqrt{ 2048 } = 45.255 ; ;
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 = 32 ; ; b = 32 ; ; c = 45.25 ; ;

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

p = a+b+c = 32+32+45.25 = 109.25 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 109.25 }{ 2 } = 54.63 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 32 * 32 }{ 2 } = 512 ; ;

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

h _a = b = 32 ; ; h _b = a = 32 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 512 }{ 45.25 } = 22.63 ; ;

7. Calculation of the inner angles of the triangle - basic use of sine function

sin alpha = fraction{ a }{ c } ; ; alpha = arcsin( fraction{ a }{ c } ) = arcsin( fraction{ 32 }{ 45.25 } ) = 45° ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 32 }{ 45.25 } ) = 45° ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 512 }{ 54.63 } = 9.37 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 32 }{ 2 * sin 45° } = 22.63 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 32**2+2 * 45.25**2 - 32**2 } }{ 2 } = 35.777 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 45.25**2+2 * 32**2 - 32**2 } }{ 2 } = 35.777 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 32**2+2 * 32**2 - 45.25**2 } }{ 2 } = 22.627 ; ;
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Trigonometry right triangle solver. You can calculate angles, sides (adjacent, opposite, hypotenuse) and area of any right-angled triangle and use it in real world to find height. A right-angled triangle is entirely determined by two independent properties. Step-by-step explanations are provided for each calculation.

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