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 = 5.36774947601   b = 1.2   c = 5.5

Area: T = 3.22204968561
Perimeter: p = 12.06774947601
Semiperimeter: s = 6.03437473801

Angle ∠ A = α = 77.39877351585° = 77°23'52″ = 1.35108453121 rad
Angle ∠ B = β = 12.60222648415° = 12°36'8″ = 0.22199510147 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 1.2
Height: hb = 5.36774947601
Height: hc = 1.17110897658

Median: ma = 2.94398129192
Median: mb = 5.40109258466
Median: mc = 2.75

Inradius: r = 0.53437473801
Circumradius: R = 2.75

Vertex coordinates: A[5.5; 0] B[0; 0] C[5.23881818182; 1.17110897658]
Centroid: CG[3.57993939394; 0.39903632553]
Coordinates of the circumscribed circle: U[2.75; 0]
Coordinates of the inscribed circle: I[4.83437473801; 0.53437473801]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 102.6022264841° = 102°36'8″ = 1.35108453121 rad
∠ B' = β' = 167.3987735159° = 167°23'52″ = 0.22199510147 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 = 1.2 ; ; c = 5.5 ; ;

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

c**2 = a**2+b**2 ; ; a = sqrt{ c**2 - b**2 } = sqrt{ 5.5**2 - 1.2**2 } = 5.367 ; ;


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 = 5.37 ; ; b = 1.2 ; ; c = 5.5 ; ;

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

p = a+b+c = 5.37+1.2+5.5 = 12.07 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12.07 }{ 2 } = 6.03 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.03 * (6.03-5.37)(6.03-1.2)(6.03-5.5) } ; ; T = sqrt{ 10.37 } = 3.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3.22 }{ 5.37 } = 1.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3.22 }{ 1.2 } = 5.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3.22 }{ 5.5 } = 1.17 ; ;

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{ 5.37**2-1.2**2-5.5**2 }{ 2 * 1.2 * 5.5 } ) = 77° 23'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.2**2-5.37**2-5.5**2 }{ 2 * 5.37 * 5.5 } ) = 12° 36'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.5**2-5.37**2-1.2**2 }{ 2 * 1.2 * 5.37 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3.22 }{ 6.03 } = 0.53 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5.37 }{ 2 * sin 77° 23'52" } = 2.75 ; ;
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