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 = 33.83767119697   b = 50.75550679546   c = 61

Area: T = 858.6922307692
Perimeter: p = 145.5921779924
Semiperimeter: s = 72.79658899622

Angle ∠ A = α = 33.6990067526° = 33°41'24″ = 0.58880026035 rad
Angle ∠ B = β = 56.3109932474° = 56°18'36″ = 0.98327937232 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 50.75550679546
Height: hb = 33.83767119697
Height: hc = 28.15438461538

Median: ma = 53.50105391777
Median: mb = 42.29658899622
Median: mc = 30.5

Inradius: r = 11.79658899622
Circumradius: R = 30.5

Vertex coordinates: A[61; 0] B[0; 0] C[18.76992307692; 28.15438461538]
Centroid: CG[26.59897435897; 9.38546153846]
Coordinates of the circumscribed circle: U[30.5; 0]
Coordinates of the inscribed circle: I[22.04108220076; 11.79658899622]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.3109932474° = 146°18'36″ = 0.58880026035 rad
∠ B' = β' = 123.6990067526° = 123°41'24″ = 0.98327937232 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 = 6 ; ; c = 61 ; ;

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

c**2 = a**2+b**2 ; ; a = sqrt{ c**2 - b**2 } = sqrt{ 61**2 - 50.755**2 } = 33.837 ; ;


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 = 33.84 ; ; b = 50.76 ; ; c = 61 ; ;

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

p = a+b+c = 33.84+50.76+61 = 145.59 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 145.59 }{ 2 } = 72.8 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 72.8 * (72.8-33.84)(72.8-50.76)(72.8-61) } ; ; T = sqrt{ 737352.48 } = 858.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 858.69 }{ 33.84 } = 50.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 858.69 }{ 50.76 } = 33.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 858.69 }{ 61 } = 28.15 ; ;

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{ 33.84**2-50.76**2-61**2 }{ 2 * 50.76 * 61 } ) = 33° 41'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 50.76**2-33.84**2-61**2 }{ 2 * 33.84 * 61 } ) = 56° 18'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 61**2-33.84**2-50.76**2 }{ 2 * 50.76 * 33.84 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 858.69 }{ 72.8 } = 11.8 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 33.84 }{ 2 * sin 33° 41'24" } = 30.5 ; ;
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