Right triangle calculator (a,b) - result

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 = 12   b = 5   c = 13

Area: T = 30
Perimeter: p = 30
Semiperimeter: s = 15

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

Height: ha = 5
Height: hb = 12
Height: hc = 4.61553846154

Median: ma = 7.81102496759
Median: mb = 12.25876506721
Median: mc = 6.5

Inradius: r = 2
Circumradius: R = 6.5

Vertex coordinates: A[13; 0] B[0; 0] C[11.07769230769; 4.61553846154]
Centroid: CG[8.02656410256; 1.53884615385]
Coordinates of the circumscribed circle: U[6.5; -0]
Coordinates of the inscribed circle: I[10; 2]

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

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How did we calculate this triangle?

1. Input data entered: cathetus a and cathetus b

a = 12 ; ; b = 5 ; ;

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{ 12**2 + 5**2 } = 13 ; ;


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 = 12 ; ; b = 5 ; ; c = 13 ; ;

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

p = a+b+c = 12+5+13 = 30 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 30 }{ 2 } = 15 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 12 * 5 }{ 2 } = 30 ; ;

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

h _a = b = 5 ; ; h _b = a = 12 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 30 }{ 13 } = 4.62 ; ;

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{ 12 }{ 13 } ) = 67° 22'49" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 5 }{ 13 } ) = 22° 37'11" ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 30 }{ 15 } = 2 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12 }{ 2 * sin 67° 22'49" } = 6.5 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5**2+2 * 13**2 - 12**2 } }{ 2 } = 7.81 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 13**2+2 * 12**2 - 5**2 } }{ 2 } = 12.258 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5**2+2 * 12**2 - 13**2 } }{ 2 } = 6.5 ; ;
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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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