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 = 43999.79328972   b = 135   c = 44000

Area: T = 2969986.021056
Perimeter: p = 88134.79328972
Semiperimeter: s = 44067.39664486

Angle ∠ A = α = 89.82442058552° = 89°49'27″ = 1.56877281402 rad
Angle ∠ B = β = 0.17657941448° = 0°10'33″ = 0.00330681866 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 135
Height: hb = 43999.79328972
Height: hc = 134.9999364571

Median: ma = 22000.31106512
Median: mb = 43999.8454673
Median: mc = 22000

Inradius: r = 67.39664486199
Circumradius: R = 22000

Vertex coordinates: A[44000; 0] B[0; 0] C[43999.58657955; 134.9999364571]
Centroid: CG[29333.19552652; 454.9997881905]
Coordinates of the circumscribed circle: U[22000; -01.3E-9]
Coordinates of the inscribed circle: I[43932.39664486; 67.39664486201]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90.17657941448° = 90°10'33″ = 1.56877281402 rad
∠ B' = β' = 179.8244205855° = 179°49'27″ = 0.00330681866 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 = 135 ; ; c = 44000 ; ;

2. From b and c we calculate side a - Pythagorean theorem:

c**2 = a**2+b**2 ; ; a = sqrt{ c**2 - b**2 } = sqrt{ 44000**2 - 135**2 } = 43999.793 ; ;


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 = 43999.79 ; ; b = 135 ; ; c = 44000 ; ;

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

p = a+b+c = 43999.79+135+44000 = 88134.79 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 88134.79 }{ 2 } = 44067.4 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 44067.4 * (44067.4-43999.79)(44067.4-135)(44067.4-44000) } ; ; T = sqrt{ 8.821 * 10**{ 12 } } = 2969986.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2969986.02 }{ 43999.79 } = 135 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2969986.02 }{ 135 } = 43999.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2969986.02 }{ 44000 } = 135 ; ;

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{ 43999.79**2-135**2-44000**2 }{ 2 * 135 * 44000 } ) = 89° 49'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 135**2-43999.79**2-44000**2 }{ 2 * 43999.79 * 44000 } ) = 0° 10'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 44000**2-43999.79**2-135**2 }{ 2 * 135 * 43999.79 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2969986.02 }{ 44067.4 } = 67.4 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 43999.79 }{ 2 * sin 89° 49'27" } = 22000 ; ;
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