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 = 24.28221465589   b = 43.70878638061   c = 50

Area: T = 530.6660377358
Perimeter: p = 117.9990010365
Semiperimeter: s = 58.99550051825

Angle ∠ A = α = 29.05546040991° = 29°3'17″ = 0.50770985044 rad
Angle ∠ B = β = 60.94553959009° = 60°56'43″ = 1.06436978224 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 43.70878638061
Height: hb = 24.28221465589
Height: hc = 21.22664150943

Median: ma = 45.36327933318
Median: mb = 32.6688287086
Median: mc = 25

Inradius: r = 8.99550051825
Circumradius: R = 25

Vertex coordinates: A[50; 0] B[0; 0] C[11.79224528302; 21.22664150943]
Centroid: CG[20.59774842767; 7.07554716981]
Coordinates of the circumscribed circle: U[25; 0]
Coordinates of the inscribed circle: I[15.28771413764; 8.99550051825]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.9455395901° = 150°56'43″ = 0.50770985044 rad
∠ B' = β' = 119.0554604099° = 119°3'17″ = 1.06436978224 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 = 50 ; ;

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

c**2 = a**2+b**2 ; ; a = sqrt{ c**2 - b**2 } = sqrt{ 50**2 - 43.708**2 } = 24.282 ; ;


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 = 24.28 ; ; b = 43.71 ; ; c = 50 ; ;

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

p = a+b+c = 24.28+43.71+50 = 117.99 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 117.99 }{ 2 } = 59 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 59 * (59-24.28)(59-43.71)(59-50) } ; ; T = sqrt{ 281600.44 } = 530.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 530.66 }{ 24.28 } = 43.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 530.66 }{ 43.71 } = 24.28 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 530.66 }{ 50 } = 21.23 ; ;

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{ 24.28**2-43.71**2-50**2 }{ 2 * 43.71 * 50 } ) = 29° 3'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 43.71**2-24.28**2-50**2 }{ 2 * 24.28 * 50 } ) = 60° 56'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 50**2-24.28**2-43.71**2 }{ 2 * 43.71 * 24.28 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 530.66 }{ 59 } = 9 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24.28 }{ 2 * sin 29° 3'17" } = 25 ; ;
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