Right triangle calculator (R,b) - result

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 circumradius R.

Right scalene triangle.

Sides: a = 19.59659179423   b = 4   c = 20

Area: T = 39.19218358845
Perimeter: p = 43.59659179423
Semiperimeter: s = 21.79879589711

Angle ∠ A = α = 78.46330409672° = 78°27'47″ = 1.3699438406 rad
Angle ∠ B = β = 11.53769590328° = 11°32'13″ = 0.20113579208 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 4
Height: hb = 19.59659179423
Height: hc = 3.91991835885

Median: ma = 10.58330052443
Median: mb = 19.69877156036
Median: mc = 10

Inradius: r = 1.79879589711
Circumradius: R = 10

Vertex coordinates: A[20; 0] B[0; 0] C[19.2; 3.91991835885]
Centroid: CG[13.06766666667; 1.30663945295]
Coordinates of the circumscribed circle: U[10; -0]
Coordinates of the inscribed circle: I[17.79879589711; 1.79879589711]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 101.5376959033° = 101°32'13″ = 1.3699438406 rad
∠ B' = β' = 168.4633040967° = 168°27'47″ = 0.20113579208 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus b circumradius R

b = 4 ; ; R = 10 ; ;

2. From circumradius R we calculate hypotenuse c:

c = 2 * R = 2 * 10 = 20 ; ;

3. 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{ 20**2 - 4**2 } = 19.596 ; ;


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 = 19.6 ; ; b = 4 ; ; c = 20 ; ;

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

p = a+b+c = 19.6+4+20 = 43.6 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43.6 }{ 2 } = 21.8 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.8 * (21.8-19.6)(21.8-4)(21.8-20) } ; ; T = sqrt{ 1536 } = 39.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 39.19 }{ 19.6 } = 4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 39.19 }{ 4 } = 19.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 39.19 }{ 20 } = 3.92 ; ;

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{ 19.6**2-4**2-20**2 }{ 2 * 4 * 20 } ) = 78° 27'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4**2-19.6**2-20**2 }{ 2 * 19.6 * 20 } ) = 11° 32'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-19.6**2-4**2 }{ 2 * 4 * 19.6 } ) = 90° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 39.19 }{ 21.8 } = 1.8 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19.6 }{ 2 * sin 78° 27'47" } = 10 ; ;
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