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 = 3.09901518458   b = 1.78441   c = 3.56882

Area: T = 2.7576569954
Perimeter: p = 8.44224518458
Semiperimeter: s = 4.22112259229

Angle ∠ A = α = 60° = 1.04771975512 rad
Angle ∠ B = β = 30° = 0.52435987756 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 1.78441
Height: hb = 3.09901518458
Height: hc = 1.54550759229

Median: ma = 2.3660142457
Median: mb = 3.21663320153
Median: mc = 1.78441

Inradius: r = 0.65330259229
Circumradius: R = 1.78441

Vertex coordinates: A[3.56882; 0] B[0; 0] C[2.676615; 1.54550759229]
Centroid: CG[2.081145; 0.51550253076]
Coordinates of the circumscribed circle: U[1.78441; 0]
Coordinates of the inscribed circle: I[2.43771259229; 0.65330259229]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120° = 1.04771975512 rad
∠ B' = β' = 150° = 0.52435987756 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 = 1.784 ; ; c = 3.568 ; ;

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{ 3.568**2 - 1.784**2 } = 3.09 ; ;


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 = 3.09 ; ; b = 1.78 ; ; c = 3.57 ; ;

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

p = a+b+c = 3.09+1.78+3.57 = 8.44 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 8.44 }{ 2 } = 4.22 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.22 * (4.22-3.09)(4.22-1.78)(4.22-3.57) } ; ; T = sqrt{ 7.6 } = 2.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.76 }{ 3.09 } = 1.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.76 }{ 1.78 } = 3.09 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.76 }{ 3.57 } = 1.55 ; ;

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{ 3.09**2-1.78**2-3.57**2 }{ 2 * 1.78 * 3.57 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.78**2-3.09**2-3.57**2 }{ 2 * 3.09 * 3.57 } ) = 30° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.57**2-3.09**2-1.78**2 }{ 2 * 1.78 * 3.09 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.76 }{ 4.22 } = 0.65 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.09 }{ 2 * sin 60° } = 1.78 ; ;
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