Right triangle calculator

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.

Right scalene triangle.

Sides: a = 6   b = 7.416   c = 9.53992377054

Area: T = 22.248
Perimeter: p = 22.95552377054
Semiperimeter: s = 11.47876188527

Angle ∠ A = α = 38.97549881449° = 38°58'30″ = 0.68802418691 rad
Angle ∠ B = β = 51.02550118551° = 51°1'30″ = 0.89105544577 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 7.416
Height: hb = 6
Height: hc = 4.66545236626

Median: ma = 87.9998159979
Median: mb = 7.0533315816
Median: mc = 4.77696188527

Inradius: r = 1.93883811473
Circumradius: R = 4.77696188527

Vertex coordinates: A[9.53992377054; 0] B[0; 0] C[3.77438864584; 4.66545236626]
Centroid: CG[4.43877080546; 1.55548412209]
Coordinates of the circumscribed circle: U[4.77696188527; -0]
Coordinates of the inscribed circle: I[4.06216188527; 1.93883811473]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.0255011855° = 141°1'30″ = 0.68802418691 rad
∠ B' = β' = 128.9754988145° = 128°58'30″ = 0.89105544577 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: and cathetus b

a = 0 ; ; b = 7.416 ; ;

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

c**2 = a**2+b**2 ; ; c = sqrt{ a**2+b**2 } = sqrt{ 6**2 + 7.416**2 } = 9.539 ; ;


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 = 6 ; ; b = 7.42 ; ; c = 9.54 ; ;

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

p = a+b+c = 6+7.42+9.54 = 22.96 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22.96 }{ 2 } = 11.48 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 6 * 7.42 }{ 2 } = 22.25 ; ;

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

h _a = b = 7.42 ; ; h _b = a = 6 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22.25 }{ 9.54 } = 4.66 ; ;

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{ 6 }{ 9.54 } ) = 38° 58'30" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 7.42 }{ 9.54 } ) = 51° 1'30" ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22.25 }{ 11.48 } = 1.94 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 38° 58'30" } = 4.77 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.42**2+2 * 9.54**2 - 6**2 } }{ 2 } = 8 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.54**2+2 * 6**2 - 7.42**2 } }{ 2 } = 7.053 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.42**2+2 * 6**2 - 9.54**2 } }{ 2 } = 4.77 ; ;
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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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