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 = 350   b = 100   c = 364.0055494464

Area: T = 17500
Perimeter: p = 814.0055494464
Semiperimeter: s = 407.0032747232

Angle ∠ A = α = 74.05546040991° = 74°3'17″ = 1.29224966678 rad
Angle ∠ B = β = 15.94553959009° = 15°56'43″ = 0.2788299659 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 100
Height: hb = 350
Height: hc = 96.15223947641

Median: ma = 201.5566443707
Median: mb = 353.5533390593
Median: mc = 182.0032747232

Inradius: r = 42.9977252768
Circumradius: R = 182.0032747232

Vertex coordinates: A[364.0055494464; 0] B[0; 0] C[336.5333381674; 96.15223947641]
Centroid: CG[233.5132958713; 32.05107982547]
Coordinates of the circumscribed circle: U[182.0032747232; 0]
Coordinates of the inscribed circle: I[307.0032747232; 42.9977252768]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 105.9455395901° = 105°56'43″ = 1.29224966678 rad
∠ B' = β' = 164.0554604099° = 164°3'17″ = 0.2788299659 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 = 350 ; ; 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{ 350**2 + 100**2 } = 364.005 ; ;


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 = 350 ; ; b = 100 ; ; c = 364.01 ; ;

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

p = a+b+c = 350+100+364.01 = 814.01 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 814.01 }{ 2 } = 407 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 407 * (407-350)(407-100)(407-364.01) } ; ; T = sqrt{ 306250000 } = 17500 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17500 }{ 350 } = 100 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17500 }{ 100 } = 350 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17500 }{ 364.01 } = 96.15 ; ;

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{ 350**2-100**2-364.01**2 }{ 2 * 100 * 364.01 } ) = 74° 3'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 100**2-350**2-364.01**2 }{ 2 * 350 * 364.01 } ) = 15° 56'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 364.01**2-350**2-100**2 }{ 2 * 100 * 350 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17500 }{ 407 } = 43 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 350 }{ 2 * sin 74° 3'17" } = 182 ; ;
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