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 = 244   b = 246   c = 346.4855208919

Area: T = 30012
Perimeter: p = 836.4855208919
Semiperimeter: s = 418.243260446

Angle ∠ A = α = 44.76661409741° = 44°45'58″ = 0.78113165534 rad
Angle ∠ B = β = 45.23438590259° = 45°14'2″ = 0.78994797734 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 246
Height: hb = 244
Height: hc = 173.2376832208

Median: ma = 274.5910604355
Median: mb = 273.2498970721
Median: mc = 173.243260446

Inradius: r = 71.75773955402
Circumradius: R = 173.243260446

Vertex coordinates: A[346.4855208919; 0] B[0; 0] C[171.8288402677; 173.2376832208]
Centroid: CG[172.7711203866; 57.74656107359]
Coordinates of the circumscribed circle: U[173.243260446; -0]
Coordinates of the inscribed circle: I[172.243260446; 71.75773955402]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.2343859026° = 135°14'2″ = 0.78113165534 rad
∠ B' = β' = 134.7666140974° = 134°45'58″ = 0.78994797734 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 = 244 ; ; b = 246 ; ;

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{ 244**2 + 246**2 } = 346.485 ; ;


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 = 244 ; ; b = 246 ; ; c = 346.49 ; ;

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

p = a+b+c = 244+246+346.49 = 836.49 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 836.49 }{ 2 } = 418.24 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 418.24 * (418.24-244)(418.24-246)(418.24-346.49) } ; ; T = sqrt{ 900720144 } = 30012 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 30012 }{ 244 } = 246 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 30012 }{ 246 } = 244 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 30012 }{ 346.49 } = 173.24 ; ;

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{ 244**2-246**2-346.49**2 }{ 2 * 246 * 346.49 } ) = 44° 45'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 246**2-244**2-346.49**2 }{ 2 * 244 * 346.49 } ) = 45° 14'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 346.49**2-244**2-246**2 }{ 2 * 246 * 244 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 30012 }{ 418.24 } = 71.76 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 244 }{ 2 * sin 44° 45'58" } = 173.24 ; ;
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