Right triangle calculator (S,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 b and area S.

Right scalene Pythagorean triangle.

Sides: a = 36   b = 48   c = 60

Area: T = 864
Perimeter: p = 144
Semiperimeter: s = 72

Angle ∠ A = α = 36.87698976458° = 36°52'12″ = 0.64435011088 rad
Angle ∠ B = β = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 48
Height: hb = 36
Height: hc = 28.8

Median: ma = 51.26440224719
Median: mb = 43.26766153056
Median: mc = 30

Inradius: r = 12
Circumradius: R = 30

Vertex coordinates: A[60; 0] B[0; 0] C[21.6; 28.8]
Centroid: CG[27.2; 9.6]
Coordinates of the circumscribed circle: U[30; 0]
Coordinates of the inscribed circle: I[24; 12]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1330102354° = 143°7'48″ = 0.64435011088 rad
∠ B' = β' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ C' = γ' = 90° = 1.57107963268 rad

Calculate another triangle




How did we calculate this triangle?

1. Input data entered: cathetus b area S

b = 48 ; ; S = 864 ; ;

2. From and cathetus b we calculate hypotenuse c - Pythagorean theorem:

c**2 = a**2+b**2 ; ; c = sqrt{ a**2+b**2 } = sqrt{ 36**2 + 48**2 } = 60 ; ;

3. From area S and hypotenuse c we calculate h:

S = fraction{ c * h }{ 2 } ; ; h = 2 * S / c = 2 * 864 / c = 28.8 ; ;


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 = 36 ; ; b = 48 ; ; c = 60 ; ;

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

p = a+b+c = 36+48+60 = 144 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 144 }{ 2 } = 72 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 72 * (72-36)(72-48)(72-60) } ; ; T = sqrt{ 746496 } = 864 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 864 }{ 36 } = 48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 864 }{ 48 } = 36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 864 }{ 60 } = 28.8 ; ;

8. 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{ 36**2-48**2-60**2 }{ 2 * 48 * 60 } ) = 36° 52'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 48**2-36**2-60**2 }{ 2 * 36 * 60 } ) = 53° 7'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 60**2-36**2-48**2 }{ 2 * 48 * 36 } ) = 90° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 864 }{ 72 } = 12 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 36 }{ 2 * sin 36° 52'12" } = 30 ; ;
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.