Right triangle calculator (a,b)

Please enter two properties of the right triangle

Use symbols: a, b, c, A, B, h, T, p, r, R


You have entered cathetus a and cathetus b.

Right scalene triangle.

Sides: a = 2.4   b = 100   c = 100.0298795854

Area: T = 120
Perimeter: p = 202.4298795854
Semiperimeter: s = 101.2144397927

Angle ∠ A = α = 1.37548347806° = 1°22'29″ = 0.02439953936 rad
Angle ∠ B = β = 88.62551652194° = 88°37'31″ = 1.54768009332 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 100
Height: hb = 2.4
Height: hc = 2.39993090985

Median: ma = 100.0077199741
Median: mb = 50.05875668606
Median: mc = 50.0144397927

Inradius: r = 1.1865602073
Circumradius: R = 50.0144397927

Vertex coordinates: A[100.0298795854; 0] B[0; 0] C[0.05875834184; 2.39993090985]
Centroid: CG[33.36221264241; 0.87997696995]
Coordinates of the circumscribed circle: U[50.0144397927; -0]
Coordinates of the inscribed circle: I[1.2144397927; 1.1865602073]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 178.6255165219° = 178°37'31″ = 0.02439953936 rad
∠ B' = β' = 91.37548347806° = 91°22'29″ = 1.54768009332 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus a cathetus b

a = 2.4 ; ; b = 100 ; ;

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

c**2 = a**2+b**2 ; ; c = sqrt{ a**2+b**2 } = sqrt{ 2.4**2 + 100**2 } = 100.029 ; ;


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 = 2.4 ; ; b = 100 ; ; c = 100.03 ; ;

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

p = a+b+c = 2.4+100+100.03 = 202.43 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 202.43 }{ 2 } = 101.21 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 101.21 * (101.21-2.4)(101.21-100)(101.21-100.03) } ; ; T = sqrt{ 14400 } = 120 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 120 }{ 2.4 } = 100 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 120 }{ 100 } = 2.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 120 }{ 100.03 } = 2.4 ; ;

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{ 2.4**2-100**2-100.03**2 }{ 2 * 100 * 100.03 } ) = 1° 22'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 100**2-2.4**2-100.03**2 }{ 2 * 2.4 * 100.03 } ) = 88° 37'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 100.03**2-2.4**2-100**2 }{ 2 * 100 * 2.4 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 120 }{ 101.21 } = 1.19 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.4 }{ 2 * sin 1° 22'29" } = 50.01 ; ;
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