Right triangle calculator (A,B,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, angle α and angle β.

Right scalene triangle.

Sides: a = 33.9411125497   b = 33.9411125497   c = 48

Area: T = 576
Perimeter: p = 115.8822250994
Semiperimeter: s = 57.9411125497

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 33.9411125497
Height: hb = 33.9411125497
Height: hc = 24

Median: ma = 37.9477331922
Median: mb = 37.9477331922
Median: mc = 24

Inradius: r = 9.9411125497
Circumradius: R = 24

Vertex coordinates: A[48; 0] B[0; 0] C[24; 24]
Centroid: CG[24; 8]
Coordinates of the circumscribed circle: U[24; 0]
Coordinates of the inscribed circle: I[24; 9.9411125497]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 135° = 0.78553981634 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: hypotenuse c angle α angle β

c = 48 ; ; alpha = 45° ; ; beta = 45° ; ;

2. From hypotenuse c and angle α we calculate cathetus a:

 sin alpha = a:c ; ; a = c * sin alpha = c * sin(45 ° ) = 33.941 ; ;

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

c**2 = a**2+b**2 ; ; b = sqrt{ c**2 - a**2 } = sqrt{ 48**2 - 33.941**2 } = 33.941 ; ;


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 = 33.94 ; ; b = 33.94 ; ; c = 48 ; ;

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

p = a+b+c = 33.94+33.94+48 = 115.88 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 115.88 }{ 2 } = 57.94 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 57.94 * (57.94-33.94)(57.94-33.94)(57.94-48) } ; ; T = sqrt{ 331776 } = 576 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 576 }{ 33.94 } = 33.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 576 }{ 33.94 } = 33.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 576 }{ 48 } = 24 ; ;

8. 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{ 33.94**2-33.94**2-48**2 }{ 2 * 33.94 * 48 } ) = 45° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 33.94**2-33.94**2-48**2 }{ 2 * 33.94 * 48 } ) = 45° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 48**2-33.94**2-33.94**2 }{ 2 * 33.94 * 33.94 } ) = 90° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 576 }{ 57.94 } = 9.94 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 33.94 }{ 2 * sin 45° } = 24 ; ;
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