Right triangle calculator (c)

Please enter two properties of the right triangle

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


You have entered hypotenuse c and perimeter p.

Right scalene Pythagorean triangle.

Sides: a = 33   b = 44   c = 55

Area: T = 726
Perimeter: p = 132
Semiperimeter: s = 66

Angle ∠ A = α = 36.87698976458° = 36°52'12″ = 0.64435011088 rad
Angle ∠ B = β = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 44
Height: hb = 33
Height: hc = 26.4

Median: ma = 46.99220205992
Median: mb = 39.66110640301
Median: mc = 27.5

Inradius: r = 11
Circumradius: R = 27.5

Vertex coordinates: A[55; 0] B[0; 0] C[19.8; 26.4]
Centroid: CG[24.93333333333; 8.8]
Coordinates of the circumscribed circle: U[27.5; 0]
Coordinates of the inscribed circle: I[22; 11]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1330102354° = 143°7'48″ = 0.64435011088 rad
∠ B' = β' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: hypotenuse c perimeter p

c = 55 ; ; p = 132 ; ;

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

c**2 = a**2+b**2 ; ; a = sqrt{ c**2 - b**2 } = sqrt{ 55**2 - 44**2 } = 33 ; ;


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 = 33 ; ; b = 44 ; ; c = 55 ; ;

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

p = a+b+c = 33+44+55 = 132 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 132 }{ 2 } = 66 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 66 * (66-33)(66-44)(66-55) } ; ; T = sqrt{ 527076 } = 726 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 726 }{ 33 } = 44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 726 }{ 44 } = 33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 726 }{ 55 } = 26.4 ; ;

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{ 33**2-44**2-55**2 }{ 2 * 44 * 55 } ) = 36° 52'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 44**2-33**2-55**2 }{ 2 * 33 * 55 } ) = 53° 7'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 55**2-33**2-44**2 }{ 2 * 44 * 33 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 726 }{ 66 } = 11 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 33 }{ 2 * sin 36° 52'12" } = 27.5 ; ;
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