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 = 3.5   b = 5.5   c = 6.51992024052

Area: T = 9.625
Perimeter: p = 15.51992024052
Semiperimeter: s = 7.76596012026

Angle ∠ A = α = 32.47111922908° = 32°28'16″ = 0.56767292175 rad
Angle ∠ B = β = 57.52988077092° = 57°31'44″ = 1.00440671093 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 5.5
Height: hb = 3.5
Height: hc = 2.95328152071

Median: ma = 5.77216981903
Median: mb = 4.45111234537
Median: mc = 3.26596012026

Inradius: r = 1.24403987974
Circumradius: R = 3.26596012026

Vertex coordinates: A[6.51992024052; 0] B[0; 0] C[1.87990642227; 2.95328152071]
Centroid: CG[2.79994222093; 0.98442717357]
Coordinates of the circumscribed circle: U[3.26596012026; 0]
Coordinates of the inscribed circle: I[2.26596012026; 1.24403987974]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.5298807709° = 147°31'44″ = 0.56767292175 rad
∠ B' = β' = 122.4711192291° = 122°28'16″ = 1.00440671093 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 = 3.5 ; ; b = 5.5 ; ;

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{ 3.5**2 + 5.5**2 } = 6.519 ; ;


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 = 3.5 ; ; b = 5.5 ; ; c = 6.52 ; ;

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

p = a+b+c = 3.5+5.5+6.52 = 15.52 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.52 }{ 2 } = 7.76 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.76 * (7.76-3.5)(7.76-5.5)(7.76-6.52) } ; ; T = sqrt{ 92.64 } = 9.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9.63 }{ 3.5 } = 5.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9.63 }{ 5.5 } = 3.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9.63 }{ 6.52 } = 2.95 ; ;

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{ 3.5**2-5.5**2-6.52**2 }{ 2 * 5.5 * 6.52 } ) = 32° 28'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.5**2-3.5**2-6.52**2 }{ 2 * 3.5 * 6.52 } ) = 57° 31'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.52**2-3.5**2-5.5**2 }{ 2 * 5.5 * 3.5 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9.63 }{ 7.76 } = 1.24 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.5 }{ 2 * sin 32° 28'16" } = 3.26 ; ;
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