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 = 14.72660208134   b = 6378.1   c = 6378.117

Area: T = 46962.0176675
Perimeter: p = 12770.94330208
Semiperimeter: s = 6385.472151041

Angle ∠ A = α = 0.13222866281° = 0°7'56″ = 0.00223088372 rad
Angle ∠ B = β = 89.86877133719° = 89°52'4″ = 1.56884874896 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 6378.1
Height: hb = 14.72660208134
Height: hc = 14.72659815632

Median: ma = 6378.104425
Median: mb = 3189.084399986
Median: mc = 3189.05985

Inradius: r = 7.35545104067
Circumradius: R = 3189.058849998

Vertex coordinates: A[6378.117; 0] B[0; 0] C[0.03439999547; 14.72659815632]
Centroid: CG[2126.055033332; 4.90986605211]
Coordinates of the circumscribed circle: U[3189.05985; 0]
Coordinates of the inscribed circle: I[7.37215104067; 7.35545104067]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 179.8687713372° = 179°52'4″ = 0.00223088372 rad
∠ B' = β' = 90.13222866281° = 90°7'56″ = 1.56884874896 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 = 6378.117 ; ;

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{ 6378.117**2 - 6378.1**2 } = 14.726 ; ;


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 = 14.73 ; ; b = 6378.1 ; ; c = 6378.12 ; ;

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

p = a+b+c = 14.73+6378.1+6378.12 = 12770.94 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12770.94 }{ 2 } = 6385.47 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6385.47 * (6385.47-14.73)(6385.47-6378.1)(6385.47-6378.12) } ; ; T = sqrt{ 2205431010.18 } = 46962.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 46962.02 }{ 14.73 } = 6378.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 46962.02 }{ 6378.1 } = 14.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 46962.02 }{ 6378.12 } = 14.73 ; ;

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{ 14.73**2-6378.1**2-6378.12**2 }{ 2 * 6378.1 * 6378.12 } ) = 0° 7'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6378.1**2-14.73**2-6378.12**2 }{ 2 * 14.73 * 6378.12 } ) = 89° 52'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6378.12**2-14.73**2-6378.1**2 }{ 2 * 6378.1 * 14.73 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 46962.02 }{ 6385.47 } = 7.35 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14.73 }{ 2 * sin 0° 7'56" } = 3189.06 ; ;
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