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 scalene triangle.

Sides: a = 40   b = 44.42   c = 59.77657174779

Area: T = 888.4
Perimeter: p = 144.1965717478
Semiperimeter: s = 72.0987858739

Angle ∠ A = α = 42.0032886546° = 42°10″ = 0.73330886656 rad
Angle ∠ B = β = 47.9977113454° = 47°59'50″ = 0.83877076612 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 44.42
Height: hb = 40
Height: hc = 29.72444445565

Median: ma = 48.71548478392
Median: mb = 45.75224217938
Median: mc = 29.8887858739

Inradius: r = 12.3222141261
Circumradius: R = 29.8887858739

Vertex coordinates: A[59.77657174779; 0] B[0; 0] C[26.76767217979; 29.72444445565]
Centroid: CG[28.84774797586; 9.90881481855]
Coordinates of the circumscribed circle: U[29.8887858739; -0]
Coordinates of the inscribed circle: I[27.6787858739; 12.3222141261]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.9977113454° = 137°59'50″ = 0.73330886656 rad
∠ B' = β' = 132.0032886546° = 132°10″ = 0.83877076612 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 = 40 ; ; b = 44.42 ; ;

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{ 40**2 + 44.42**2 } = 59.776 ; ;


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 = 40 ; ; b = 44.42 ; ; c = 59.78 ; ;

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

p = a+b+c = 40+44.42+59.78 = 144.2 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 144.2 }{ 2 } = 72.1 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 72.1 * (72.1-40)(72.1-44.42)(72.1-59.78) } ; ; T = sqrt{ 789254.56 } = 888.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 888.4 }{ 40 } = 44.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 888.4 }{ 44.42 } = 40 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 888.4 }{ 59.78 } = 29.72 ; ;

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{ 40**2-44.42**2-59.78**2 }{ 2 * 44.42 * 59.78 } ) = 42° 10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 44.42**2-40**2-59.78**2 }{ 2 * 40 * 59.78 } ) = 47° 59'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 59.78**2-40**2-44.42**2 }{ 2 * 44.42 * 40 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 888.4 }{ 72.1 } = 12.32 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 40 }{ 2 * sin 42° 10" } = 29.89 ; ;
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