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 = 17.30876923077   b = 41.53884615385   c = 45

Area: T = 359.4677455621
Perimeter: p = 103.8466153846
Semiperimeter: s = 51.92330769231

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 = 41.53884615385
Height: hb = 17.30876923077
Height: hc = 15.97663313609

Median: ma = 42.43303292497
Median: mb = 27.03554796474
Median: mc = 22.5

Inradius: r = 6.92330769231
Circumradius: R = 22.5

Vertex coordinates: A[45; 0] B[0; 0] C[6.65768047337; 15.97663313609]
Centroid: CG[17.21989349112; 5.3255443787]
Coordinates of the circumscribed circle: U[22.5; -0]
Coordinates of the inscribed circle: I[10.38546153846; 6.92330769231]

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

Calculate another triangle




How did we calculate this triangle?

1. Input data entered: cathetus b hypotenuse c

b = 5 ; ; c = 45 ; ;

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

c**2 = a**2+b**2 ; ; a = sqrt{ c**2 - b**2 } = sqrt{ 45**2 - 41.538**2 } = 17.308 ; ;


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 = 17.31 ; ; b = 41.54 ; ; c = 45 ; ;

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

p = a+b+c = 17.31+41.54+45 = 103.85 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 103.85 }{ 2 } = 51.92 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 51.92 * (51.92-17.31)(51.92-41.54)(51.92-45) } ; ; T = sqrt{ 129216.85 } = 359.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 359.47 }{ 17.31 } = 41.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 359.47 }{ 41.54 } = 17.31 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 359.47 }{ 45 } = 15.98 ; ;

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{ 17.31**2-41.54**2-45**2 }{ 2 * 41.54 * 45 } ) = 22° 37'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 41.54**2-17.31**2-45**2 }{ 2 * 17.31 * 45 } ) = 67° 22'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 45**2-17.31**2-41.54**2 }{ 2 * 41.54 * 17.31 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 359.47 }{ 51.92 } = 6.92 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17.31 }{ 2 * sin 22° 37'11" } = 22.5 ; ;
Trigonometry right triangle solver. Find the hypotenuse c of a triangle - calculator. Area T of right triangle calculator.

Calculate right triangle by:




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.