Right triangle calculator (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 cathetus b and hypotenuse c.

Right scalene Pythagorean triangle.

Sides: a = 46.2   b = 61.6   c = 77

Area: T = 1422.96
Perimeter: p = 184.8
Semiperimeter: s = 92.4

Angle ∠ A = α = 36.87698976458° = 36°52'12″ = 0.64435011088 rad
Angle ∠ B = β = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 61.6
Height: hb = 46.2
Height: hc = 36.96

Median: ma = 65.78988288389
Median: mb = 55.52554896421
Median: mc = 38.5

Inradius: r = 15.4
Circumradius: R = 38.5

Vertex coordinates: A[77; 0] B[0; 0] C[27.72; 36.96]
Centroid: CG[34.90766666667; 12.32]
Coordinates of the circumscribed circle: U[38.5; 0]
Coordinates of the inscribed circle: I[30.8; 15.4]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1330102354° = 143°7'48″ = 0.64435011088 rad
∠ B' = β' = 126.8769897646° = 126°52'12″ = 0.9277295218 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

b = 3 ; ; c = 77 ; ;

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

c**2 = a**2+b**2 ; ; a = sqrt{ c**2 - b**2 } = sqrt{ 77**2 - 61.6**2 } = 46.2 ; ;


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 = 46.2 ; ; b = 61.6 ; ; c = 77 ; ;

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

p = a+b+c = 46.2+61.6+77 = 184.8 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 184.8 }{ 2 } = 92.4 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 92.4 * (92.4-46.2)(92.4-61.6)(92.4-77) } ; ; T = sqrt{ 2024815.16 } = 1422.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1422.96 }{ 46.2 } = 61.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1422.96 }{ 61.6 } = 46.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1422.96 }{ 77 } = 36.96 ; ;

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{ 46.2**2-61.6**2-77**2 }{ 2 * 61.6 * 77 } ) = 36° 52'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 61.6**2-46.2**2-77**2 }{ 2 * 46.2 * 77 } ) = 53° 7'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 77**2-46.2**2-61.6**2 }{ 2 * 61.6 * 46.2 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1422.96 }{ 92.4 } = 15.4 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 46.2 }{ 2 * sin 36° 52'12" } = 38.5 ; ;
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