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 = 14.28663380889   b = 6378.1   c = 6378.116

Area: T = 45559.84664824
Perimeter: p = 12770.50223381
Semiperimeter: s = 6385.251116904

Angle ∠ A = α = 0.12883368885° = 0°7'42″ = 0.00222399013 rad
Angle ∠ B = β = 89.87216631115° = 89°52'18″ = 1.56985564255 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 6378.1
Height: hb = 14.28663380889
Height: hc = 14.28663022505

Median: ma = 6378.104
Median: mb = 3189.082199988
Median: mc = 3189.058

Inradius: r = 7.13551690444
Circumradius: R = 3189.058799995

Vertex coordinates: A[6378.116; 0] B[0; 0] C[0.03219999599; 14.28663022505]
Centroid: CG[2126.049933332; 4.76221007502]
Coordinates of the circumscribed circle: U[3189.058; 0]
Coordinates of the inscribed circle: I[7.15111690444; 7.13551690444]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 179.8721663112° = 179°52'18″ = 0.00222399013 rad
∠ B' = β' = 90.12883368885° = 90°7'42″ = 1.56985564255 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 = 6378.116 ; ;

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{ 6378.116**2 - 6378.1**2 } = 14.286 ; ;


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 = 14.29 ; ; b = 6378.1 ; ; c = 6378.12 ; ;

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

p = a+b+c = 14.29+6378.1+6378.12 = 12770.5 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12770.5 }{ 2 } = 6385.25 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6385.25 * (6385.25-14.29)(6385.25-6378.1)(6385.25-6378.12) } ; ; T = sqrt{ 2075699611.5 } = 45559.85 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 45559.85 }{ 14.29 } = 6378.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 45559.85 }{ 6378.1 } = 14.29 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 45559.85 }{ 6378.12 } = 14.29 ; ;

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{ 14.29**2-6378.1**2-6378.12**2 }{ 2 * 6378.1 * 6378.12 } ) = 0° 7'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6378.1**2-14.29**2-6378.12**2 }{ 2 * 14.29 * 6378.12 } ) = 89° 52'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6378.12**2-14.29**2-6378.1**2 }{ 2 * 6378.1 * 14.29 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 45559.85 }{ 6385.25 } = 7.14 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14.29 }{ 2 * sin 0° 7'42" } = 3189.06 ; ;
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