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 = 6.50876877614   b = 1.1   c = 6.6

Area: T = 3.57992282688
Perimeter: p = 14.20876877614
Semiperimeter: s = 7.10438438807

Angle ∠ A = α = 80.40659317731° = 80°24'21″ = 1.40333482476 rad
Angle ∠ B = β = 9.59440682269° = 9°35'39″ = 0.16774480792 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 1.1
Height: hb = 6.50876877614
Height: hc = 1.08546146269

Median: ma = 3.43547488991
Median: mb = 6.53108881479
Median: mc = 3.3

Inradius: r = 0.50438438807
Circumradius: R = 3.3

Vertex coordinates: A[6.6; 0] B[0; 0] C[6.41766666667; 1.08546146269]
Centroid: CG[4.33988888889; 0.3621538209]
Coordinates of the circumscribed circle: U[3.3; -0]
Coordinates of the inscribed circle: I[6.00438438807; 0.50438438807]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 99.59440682269° = 99°35'39″ = 1.40333482476 rad
∠ B' = β' = 170.4065931773° = 170°24'21″ = 0.16774480792 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 = 1.1 ; ; c = 6.6 ; ;

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{ 6.6**2 - 1.1**2 } = 6.508 ; ;


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 = 6.51 ; ; b = 1.1 ; ; c = 6.6 ; ;

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

p = a+b+c = 6.51+1.1+6.6 = 14.21 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 14.21 }{ 2 } = 7.1 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.1 * (7.1-6.51)(7.1-1.1)(7.1-6.6) } ; ; T = sqrt{ 12.81 } = 3.58 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3.58 }{ 6.51 } = 1.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3.58 }{ 1.1 } = 6.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3.58 }{ 6.6 } = 1.08 ; ;

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{ 6.51**2-1.1**2-6.6**2 }{ 2 * 1.1 * 6.6 } ) = 80° 24'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.1**2-6.51**2-6.6**2 }{ 2 * 6.51 * 6.6 } ) = 9° 35'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.6**2-6.51**2-1.1**2 }{ 2 * 1.1 * 6.51 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3.58 }{ 7.1 } = 0.5 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.51 }{ 2 * sin 80° 24'21" } = 3.3 ; ;
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