Right triangle calculator (a) - 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 area T.

Right scalene triangle.

Sides: a = 2   b = 6   c = 6.32545553203

Area: T = 6
Perimeter: p = 14.32545553203
Semiperimeter: s = 7.16222776602

Angle ∠ A = α = 18.43549488229° = 18°26'6″ = 0.32217505544 rad
Angle ∠ B = β = 71.56550511771° = 71°33'54″ = 1.24990457724 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 6
Height: hb = 2
Height: hc = 1.89773665961

Median: ma = 6.08327625303
Median: mb = 3.60655512755
Median: mc = 3.16222776602

Inradius: r = 0.83877223398
Circumradius: R = 3.16222776602

Vertex coordinates: A[6.32545553203; 0] B[0; 0] C[0.6322455532; 1.89773665961]
Centroid: CG[2.31990036175; 0.6322455532]
Coordinates of the circumscribed circle: U[3.16222776602; -0]
Coordinates of the inscribed circle: I[1.16222776602; 0.83877223398]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.5655051177° = 161°33'54″ = 0.32217505544 rad
∠ B' = β' = 108.4354948823° = 108°26'6″ = 1.24990457724 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus a area T

a = 2 ; ; S = 6 ; ;

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

c**2 = a**2+b**2 ; ; c = sqrt{ a**2+b**2 } = sqrt{ 2**2 + 6**2 } = 6.325 ; ;

3. From area T and hypotenuse c we calculate h:

S = fraction{ c * h }{ 2 } ; ; h = 2 * S / c = 2 * 6 / c = 1.897 ; ;


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 = 2 ; ; b = 6 ; ; c = 6.32 ; ;

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

p = a+b+c = 2+6+6.32 = 14.32 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 14.32 }{ 2 } = 7.16 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.16 * (7.16-2)(7.16-6)(7.16-6.32) } ; ; T = sqrt{ 36 } = 6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6 }{ 2 } = 6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6 }{ 6 } = 2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6 }{ 6.32 } = 1.9 ; ;

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{ 2**2-6**2-6.32**2 }{ 2 * 6 * 6.32 } ) = 18° 26'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6**2-2**2-6.32**2 }{ 2 * 2 * 6.32 } ) = 71° 33'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.32**2-2**2-6**2 }{ 2 * 6 * 2 } ) = 90° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6 }{ 7.16 } = 0.84 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 18° 26'6" } = 3.16 ; ;
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