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 = 299   b = 180   c = 349

Area: T = 26910
Perimeter: p = 828
Semiperimeter: s = 414

Angle ∠ A = α = 58.95217780065° = 58°57'6″ = 1.02989026261 rad
Angle ∠ B = β = 31.04882219935° = 31°2'54″ = 0.54218937007 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 180
Height: hb = 299
Height: hc = 154.2122034384

Median: ma = 233.9887713353
Median: mb = 312.2521501197
Median: mc = 174.5

Inradius: r = 65
Circumradius: R = 174.5

Vertex coordinates: A[349; 0] B[0; 0] C[256.1633323782; 154.2122034384]
Centroid: CG[201.7211107927; 51.40440114613]
Coordinates of the circumscribed circle: U[174.5; 0]
Coordinates of the inscribed circle: I[234; 65]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.0488221994° = 121°2'54″ = 1.02989026261 rad
∠ B' = β' = 148.9521778006° = 148°57'6″ = 0.54218937007 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 = 299 ; ; b = 180 ; ;

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{ 299**2 + 180**2 } = 349 ; ;


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 = 299 ; ; b = 180 ; ; c = 349 ; ;

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

p = a+b+c = 299+180+349 = 828 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 828 }{ 2 } = 414 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 414 * (414-299)(414-180)(414-349) } ; ; T = sqrt{ 724148100 } = 26910 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26910 }{ 299 } = 180 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26910 }{ 180 } = 299 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26910 }{ 349 } = 154.21 ; ;

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{ 299**2-180**2-349**2 }{ 2 * 180 * 349 } ) = 58° 57'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 180**2-299**2-349**2 }{ 2 * 299 * 349 } ) = 31° 2'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 349**2-299**2-180**2 }{ 2 * 180 * 299 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26910 }{ 414 } = 65 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 299 }{ 2 * sin 58° 57'6" } = 174.5 ; ;
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