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 triangle.

Sides: a = 17.30876923077   b = 41.53884615385   c = 45

Area: T = 359.4677455621
Perimeter: p = 103.8466153846
Semiperimeter: s = 51.92330769231

Angle ∠ A = α = 22.6219864948° = 22°37'11″ = 0.39547911197 rad
Angle ∠ B = β = 67.3880135052° = 67°22'49″ = 1.17660052071 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 41.53884615385
Height: hb = 17.30876923077
Height: hc = 15.97663313609

Median: ma = 42.43303292497
Median: mb = 27.03554796474
Median: mc = 22.5

Inradius: r = 6.92330769231
Circumradius: R = 22.5

Vertex coordinates: A[45; 0] B[0; 0] C[6.65768047337; 15.97663313609]
Centroid: CG[17.21989349112; 5.3255443787]
Coordinates of the circumscribed circle: U[22.5; -0]
Coordinates of the inscribed circle: I[10.38546153846; 6.92330769231]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.3880135052° = 157°22'49″ = 0.39547911197 rad
∠ B' = β' = 112.6219864948° = 112°37'11″ = 1.17660052071 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus b and hypotenuse c

b = 0.417 ; ; c = 45 ; ;

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

c**2 = a**2+b**2 ; ; a = sqrt{ c**2 - b**2 } = sqrt{ 45**2 - 41.538**2 } = 17.308 ; ;
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 = 17.31 ; ; b = 41.54 ; ; c = 45 ; ;

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

p = a+b+c = 17.31+41.54+45 = 103.85 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 103.85 }{ 2 } = 51.92 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 17.31 * 41.54 }{ 2 } = 359.47 ; ;

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

h _a = b = 41.54 ; ; h _b = a = 17.31 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 359.47 }{ 45 } = 15.98 ; ;

7. Calculation of the inner angles of the triangle - basic use of sine function

 sin alpha = fraction{ a }{ c } ; ; alpha = arcsin( fraction{ a }{ c } ) = arcsin( fraction{ 17.31 }{ 45 } ) = 22° 37'11" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 41.54 }{ 45 } ) = 67° 22'49" ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 359.47 }{ 51.92 } = 6.92 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 17.31 }{ 2 * sin 22° 37'11" } = 22.5 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 41.54**2+2 * 45**2 - 17.31**2 } }{ 2 } = 42.43 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 45**2+2 * 17.31**2 - 41.54**2 } }{ 2 } = 27.035 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 41.54**2+2 * 17.31**2 - 45**2 } }{ 2 } = 22.5 ; ;
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Trigonometry right triangle solver. You can calculate angles, sides (adjacent, opposite, hypotenuse) and area of any right-angled triangle and use it in real world to find height. A right-angled triangle is entirely determined by two independent properties. Step-by-step explanations are provided for each calculation.

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