Right triangle calculator (b,c,h)

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, hypotenuse c and height h.

Right scalene triangle.

Sides: a = 0.62443468587   b = 0.72   c = 0.953

Area: T = 0.22547648691
Perimeter: p = 2.29773468587
Semiperimeter: s = 1.14986734294

Angle ∠ A = α = 40.93301421058° = 40°55'49″ = 0.71443657431 rad
Angle ∠ B = β = 49.07698578942° = 49°4'11″ = 0.85664305837 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 0.72
Height: hb = 0.62443468587
Height: hc = 0.47216996204

Median: ma = 0.78547625437
Median: mb = 0.72107003538
Median: mc = 0.47765

Inradius: r = 0.19656734294
Circumradius: R = 0.47765

Vertex coordinates: A[0.953; 0] B[0; 0] C[0.40990335782; 0.47216996204]
Centroid: CG[0.45440111927; 0.15772332068]
Coordinates of the circumscribed circle: U[0.47765; 0]
Coordinates of the inscribed circle: I[0.42986734294; 0.19656734294]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.0769857894° = 139°4'11″ = 0.71443657431 rad
∠ B' = β' = 130.9330142106° = 130°55'49″ = 0.85664305837 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus b hypotenuse c height h

b = 0.72 ; ; c = 0.953 ; ; hc = 0.625 ; ;

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

c**2 = a**2+b**2 ; ; a = sqrt{ c**2 - b**2 } = sqrt{ 0.953**2 - 0.72**2 } = 0.624 ; ;


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 = 0.62 ; ; b = 0.72 ; ; c = 0.95 ; ;

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

p = a+b+c = 0.62+0.72+0.95 = 2.3 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2.3 }{ 2 } = 1.15 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1.15 * (1.15-0.62)(1.15-0.72)(1.15-0.95) } ; ; T = sqrt{ 0.05 } = 0.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.22 }{ 0.62 } = 0.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.22 }{ 0.72 } = 0.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.22 }{ 0.95 } = 0.47 ; ;

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{ 0.62**2-0.72**2-0.95**2 }{ 2 * 0.72 * 0.95 } ) = 40° 55'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 0.72**2-0.62**2-0.95**2 }{ 2 * 0.62 * 0.95 } ) = 49° 4'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.95**2-0.62**2-0.72**2 }{ 2 * 0.72 * 0.62 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.22 }{ 1.15 } = 0.2 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 0.62 }{ 2 * sin 40° 55'49" } = 0.48 ; ;
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