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 b and angle α.

Right scalene triangle.

Sides: a = 0.02   b = 0.02   c = 0.02882842712

Area: T = 00.0002
Perimeter: p = 0.06882842712
Semiperimeter: s = 0.03441421356

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

Height: ha = 0.02
Height: hb = 0.02
Height: hc = 0.01441421356

Median: ma = 0.02223606798
Median: mb = 0.02223606798
Median: mc = 0.01441421356

Inradius: r = 0.00658578644
Circumradius: R = 0.01441421356

Vertex coordinates: A[0.02882842712; 0] B[0; 0] C[0.01441421356; 0.01441421356]
Centroid: CG[0.01441421356; 0.00547140452]
Coordinates of the circumscribed circle: U[0.01441421356; 0]
Coordinates of the inscribed circle: I[0.01441421356; 0.00658578644]

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: cathetus b angle α

b = 0.02 ; ; alpha = 45° ; ;

2. From angle α we calculate angle β:

 alpha + beta + 90° = 180° ; ; beta = 90° - alpha = 90° - 45 ° = 45 ° ; ;

3. From cathetus b and angle α we calculate hypotenuse c:

 cos alpha = b:c ; ; c = b/ cos alpha = b/ cos(45 ° ) = 0.028 ; ;

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

 sin alpha = a:c ; ; a = c * sin alpha = c * sin(45 ° ) = 0.02 ; ;


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 = 0.02 ; ; b = 0.02 ; ; c = 0.03 ; ;

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

p = a+b+c = 0.02+0.02+0.03 = 0.07 ; ;

6. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 0.07 }{ 2 } = 0.03 ; ;

7. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.03 * (0.03-0.02)(0.03-0.02)(0.03-0.03) } ; ; T = sqrt{ 0 } = 0 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0 }{ 0.02 } = 0.02 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0 }{ 0.02 } = 0.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0 }{ 0.03 } = 0.01 ; ;

9. 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{ 0.02**2-0.02**2-0.03**2 }{ 2 * 0.02 * 0.03 } ) = 45° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 0.02**2-0.02**2-0.03**2 }{ 2 * 0.02 * 0.03 } ) = 45° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.03**2-0.02**2-0.02**2 }{ 2 * 0.02 * 0.02 } ) = 90° ; ;

10. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0 }{ 0.03 } = 0.01 ; ;

11. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 0.02 }{ 2 * sin 45° } = 0.01 ; ;
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