Right triangle calculator (b,c)

Please enter two properties of the right triangle

Use symbols: a, b, c, A, B, h, T, p, r, R


You have entered cathetus b and hypotenuse c.

Right scalene triangle.

Sides: a = 18.07769230769   b = 43.38546153846   c = 47

Area: T = 392.1330177515
Perimeter: p = 108.4621538461
Semiperimeter: s = 54.23107692308

Angle ∠ A = α = 22.6219864948° = 22°37'11″ = 0.39547911197 rad
Angle ∠ B = β = 67.3880135052° = 67°22'49″ = 1.17660052071 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 43.38546153846
Height: hb = 18.07769230769
Height: hc = 16.68663905325

Median: ma = 44.31661216608
Median: mb = 28.23770565206
Median: mc = 23.5

Inradius: r = 7.23107692308
Circumradius: R = 23.5

Vertex coordinates: A[47; 0] B[0; 0] C[6.95326627219; 16.68663905325]
Centroid: CG[17.98442209073; 5.56221301775]
Coordinates of the circumscribed circle: U[23.5; 0]
Coordinates of the inscribed circle: I[10.84661538462; 7.23107692308]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.3880135052° = 157°22'49″ = 0.39547911197 rad
∠ B' = β' = 112.6219864948° = 112°37'11″ = 1.17660052071 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus b hypotenuse c

b = 5 ; ; c = 47 ; ;

2. From b and c we calculate side a - Pythagorean theorem:

c**2 = a**2+b**2 ; ; a = sqrt{ c**2 - b**2 } = sqrt{ 47**2 - 43.385**2 } = 18.077 ; ;


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 = 18.08 ; ; b = 43.38 ; ; c = 47 ; ;

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

p = a+b+c = 18.08+43.38+47 = 108.46 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 108.46 }{ 2 } = 54.23 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 54.23 * (54.23-18.08)(54.23-43.38)(54.23-47) } ; ; T = sqrt{ 153766.08 } = 392.13 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 392.13 }{ 18.08 } = 43.38 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 392.13 }{ 43.38 } = 18.08 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 392.13 }{ 47 } = 16.69 ; ;

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{ 18.08**2-43.38**2-47**2 }{ 2 * 43.38 * 47 } ) = 22° 37'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 43.38**2-18.08**2-47**2 }{ 2 * 18.08 * 47 } ) = 67° 22'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 47**2-18.08**2-43.38**2 }{ 2 * 43.38 * 18.08 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 392.13 }{ 54.23 } = 7.23 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18.08 }{ 2 * sin 22° 37'11" } = 23.5 ; ;
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