Right triangle calculator (a,p) - result

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 perimeter p.

Right scalene triangle.

Sides: a = 43   b = 26.49435064935   c = 50.50664935065

Area: T = 569.611038961
Perimeter: p = 120
Semiperimeter: s = 60

Angle ∠ A = α = 58.3621612105° = 58°21'42″ = 1.0198602288 rad
Angle ∠ B = β = 31.6388387895° = 31°38'18″ = 0.55221940388 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 26.49435064935
Height: hb = 43
Height: hc = 22.55659269735

Median: ma = 34.12197286965
Median: mb = 44.99441826415
Median: mc = 25.25332467532

Inradius: r = 9.49435064935
Circumradius: R = 25.25332467532

Vertex coordinates: A[50.50664935065; 0] B[0; 0] C[36.60991540242; 22.55659269735]
Centroid: CG[29.03985491769; 7.51986423245]
Coordinates of the circumscribed circle: U[25.25332467532; 0]
Coordinates of the inscribed circle: I[33.50664935065; 9.49435064935]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.6388387895° = 121°38'18″ = 1.0198602288 rad
∠ B' = β' = 148.3621612105° = 148°21'42″ = 0.55221940388 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus a perimeter p

a = 43 ; ; p = 120 ; ;

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

c**2 = a**2+b**2 ; ; c = sqrt{ a**2+b**2 } = sqrt{ 43**2 + 26.494**2 } = 50.506 ; ;


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 = 43 ; ; b = 26.49 ; ; c = 50.51 ; ;

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

p = a+b+c = 43+26.49+50.51 = 120 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 120 }{ 2 } = 60 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 60 * (60-43)(60-26.49)(60-50.51) } ; ; T = sqrt{ 324456 } = 569.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 569.61 }{ 43 } = 26.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 569.61 }{ 26.49 } = 43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 569.61 }{ 50.51 } = 22.56 ; ;

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{ 43**2-26.49**2-50.51**2 }{ 2 * 26.49 * 50.51 } ) = 58° 21'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26.49**2-43**2-50.51**2 }{ 2 * 43 * 50.51 } ) = 31° 38'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 50.51**2-43**2-26.49**2 }{ 2 * 26.49 * 43 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 569.61 }{ 60 } = 9.49 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 43 }{ 2 * sin 58° 21'42" } = 25.25 ; ;
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