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 = 91   b = 60   c = 109

Area: T = 2730
Perimeter: p = 260
Semiperimeter: s = 130

Angle ∠ A = α = 56.6021511532° = 56°36'5″ = 0.98878827378 rad
Angle ∠ B = β = 33.3988488468° = 33°23'55″ = 0.5832913589 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 60
Height: hb = 91
Height: hc = 50.09217431193

Median: ma = 75.30110624095
Median: mb = 95.81875349297
Median: mc = 54.5

Inradius: r = 21
Circumradius: R = 54.5

Vertex coordinates: A[109; 0] B[0; 0] C[75.97224770642; 50.09217431193]
Centroid: CG[61.65774923547; 16.69772477064]
Coordinates of the circumscribed circle: U[54.5; 0]
Coordinates of the inscribed circle: I[70; 21]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 123.3988488468° = 123°23'55″ = 0.98878827378 rad
∠ B' = β' = 146.6021511532° = 146°36'5″ = 0.5832913589 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 = 91 ; ; b = 60 ; ;

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{ 91**2 + 60**2 } = 109 ; ;


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 = 91 ; ; b = 60 ; ; c = 109 ; ;

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

p = a+b+c = 91+60+109 = 260 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 260 }{ 2 } = 130 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 130 * (130-91)(130-60)(130-109) } ; ; T = sqrt{ 7452900 } = 2730 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2730 }{ 91 } = 60 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2730 }{ 60 } = 91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2730 }{ 109 } = 50.09 ; ;

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{ 91**2-60**2-109**2 }{ 2 * 60 * 109 } ) = 56° 36'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 60**2-91**2-109**2 }{ 2 * 91 * 109 } ) = 33° 23'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 109**2-91**2-60**2 }{ 2 * 60 * 91 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2730 }{ 130 } = 21 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 91 }{ 2 * sin 56° 36'5" } = 54.5 ; ;
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