Right triangle calculator (b,v)

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 height h.

Right scalene triangle.

Sides: a = 11.54397349427   b = 17.3   c = 20.79655640113

Area: T = 99.81987072541
Perimeter: p = 49.6355298954
Semiperimeter: s = 24.8187649477

Angle ∠ A = α = 33.70547429507° = 33°42'17″ = 0.5888258738 rad
Angle ∠ B = β = 56.29552570493° = 56°17'43″ = 0.98325375888 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 17.3
Height: hb = 11.54397349427
Height: hc = 9.6

Median: ma = 18.23768136098
Median: mb = 14.42217884656
Median: mc = 10.39877820056

Inradius: r = 4.02220854657
Circumradius: R = 10.39877820056

Vertex coordinates: A[20.79655640113; 0] B[0; 0] C[6.40435523381; 9.6]
Centroid: CG[9.06663721165; 3.2]
Coordinates of the circumscribed circle: U[10.39877820056; -0]
Coordinates of the inscribed circle: I[7.5187649477; 4.02220854657]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.2955257049° = 146°17'43″ = 0.5888258738 rad
∠ B' = β' = 123.7054742951° = 123°42'17″ = 0.98325375888 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus b height h

b = 17.3 ; ; hc = 9.6 ; ;

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

c**2 = a**2+b**2 ; ; a = sqrt{ c**2 - b**2 } = sqrt{ 20.796**2 - 17.3**2 } = 11.54 ; ;


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 = 11.54 ; ; b = 17.3 ; ; c = 20.8 ; ;

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

p = a+b+c = 11.54+17.3+20.8 = 49.64 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49.64 }{ 2 } = 24.82 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.82 * (24.82-11.54)(24.82-17.3)(24.82-20.8) } ; ; T = sqrt{ 9963.77 } = 99.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 99.82 }{ 11.54 } = 17.3 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 99.82 }{ 17.3 } = 11.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 99.82 }{ 20.8 } = 9.6 ; ;

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{ 11.54**2-17.3**2-20.8**2 }{ 2 * 17.3 * 20.8 } ) = 33° 42'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17.3**2-11.54**2-20.8**2 }{ 2 * 11.54 * 20.8 } ) = 56° 17'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20.8**2-11.54**2-17.3**2 }{ 2 * 17.3 * 11.54 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 99.82 }{ 24.82 } = 4.02 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11.54 }{ 2 * sin 33° 42'17" } = 10.4 ; ;
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