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 = 12.37223297724   b = 6378.1   c = 6378.112

Area: T = 39455.97882608
Perimeter: p = 12768.58443298
Semiperimeter: s = 6384.292216489

Angle ∠ A = α = 0.11111430347° = 0°6'40″ = 0.00219398119 rad
Angle ∠ B = β = 89.88988569653° = 89°53'20″ = 1.56988565149 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 6378.1
Height: hb = 12.37223297724
Height: hc = 12.37223064947

Median: ma = 6378.103
Median: mb = 3189.074399993
Median: mc = 3189.056

Inradius: r = 6.18801648862
Circumradius: R = 3189.056600001

Vertex coordinates: A[6378.112; 0] B[0; 0] C[0.02439999774; 12.37223064947]
Centroid: CG[2126.045533333; 4.12441021649]
Coordinates of the circumscribed circle: U[3189.056; 0]
Coordinates of the inscribed circle: I[6.19221648862; 6.18801648862]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 179.8898856965° = 179°53'20″ = 0.00219398119 rad
∠ B' = β' = 90.11111430347° = 90°6'40″ = 1.56988565149 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 = 6378.1 ; ; c = 6378.112 ; ;

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{ 6378.112**2 - 6378.1**2 } = 12.372 ; ;


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 = 12.37 ; ; b = 6378.1 ; ; c = 6378.11 ; ;

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

p = a+b+c = 12.37+6378.1+6378.11 = 12768.58 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12768.58 }{ 2 } = 6384.29 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6384.29 * (6384.29-12.37)(6384.29-6378.1)(6384.29-6378.11) } ; ; T = sqrt{ 1556774220.51 } = 39455.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 39455.98 }{ 12.37 } = 6378.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 39455.98 }{ 6378.1 } = 12.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 39455.98 }{ 6378.11 } = 12.37 ; ;

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{ 12.37**2-6378.1**2-6378.11**2 }{ 2 * 6378.1 * 6378.11 } ) = 0° 6'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6378.1**2-12.37**2-6378.11**2 }{ 2 * 12.37 * 6378.11 } ) = 89° 53'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6378.11**2-12.37**2-6378.1**2 }{ 2 * 6378.1 * 12.37 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 39455.98 }{ 6384.29 } = 6.18 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12.37 }{ 2 * sin 0° 6'40" } = 3189.06 ; ;
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