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 a and cathetus b.

Right scalene triangle.

Sides: a = 50   b = 156.6   c = 164.3888442416

Area: T = 3915
Perimeter: p = 370.9888442416
Semiperimeter: s = 185.4944221208

Angle ∠ A = α = 17.70774924454° = 17°42'27″ = 0.30990540454 rad
Angle ∠ B = β = 72.29325075546° = 72°17'33″ = 1.26217422814 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 156.6
Height: hb = 50
Height: hc = 47.63110857681

Median: ma = 158.5832975127
Median: mb = 92.90325833871
Median: mc = 82.19442212081

Inradius: r = 21.10657787919
Circumradius: R = 82.19442212081

Vertex coordinates: A[164.3888442416; 0] B[0; 0] C[15.20878817906; 47.63110857681]
Centroid: CG[59.86554414022; 15.87770285894]
Coordinates of the circumscribed circle: U[82.19442212081; -0]
Coordinates of the inscribed circle: I[28.89442212081; 21.10657787919]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.2932507555° = 162°17'33″ = 0.30990540454 rad
∠ B' = β' = 107.7077492445° = 107°42'27″ = 1.26217422814 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus a cathetus b

a = 50 ; ; b = 156.6 ; ;

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

c**2 = a**2+b**2 ; ; c = sqrt{ a**2+b**2 } = sqrt{ 50**2 + 156.6**2 } = 164.388 ; ;


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 = 50 ; ; b = 156.6 ; ; c = 164.39 ; ;

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

p = a+b+c = 50+156.6+164.39 = 370.99 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 370.99 }{ 2 } = 185.49 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 185.49 * (185.49-50)(185.49-156.6)(185.49-164.39) } ; ; T = sqrt{ 15327225 } = 3915 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3915 }{ 50 } = 156.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3915 }{ 156.6 } = 50 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3915 }{ 164.39 } = 47.63 ; ;

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{ 50**2-156.6**2-164.39**2 }{ 2 * 156.6 * 164.39 } ) = 17° 42'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 156.6**2-50**2-164.39**2 }{ 2 * 50 * 164.39 } ) = 72° 17'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 164.39**2-50**2-156.6**2 }{ 2 * 156.6 * 50 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3915 }{ 185.49 } = 21.11 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 50 }{ 2 * sin 17° 42'27" } = 82.19 ; ;
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