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 = 14.01766376753   b = 10.3   c = 17.39441407296

Area: T = 72.18656840278
Perimeter: p = 41.71107784049
Semiperimeter: s = 20.85553892024

Angle ∠ A = α = 53.69900288859° = 53°41'24″ = 0.93770677795 rad
Angle ∠ B = β = 36.31099711141° = 36°18'36″ = 0.63437285472 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 10.3
Height: hb = 14.01766376753
Height: hc = 8.3

Median: ma = 12.45881913988
Median: mb = 14.93328038801
Median: mc = 8.69770703648

Inradius: r = 3.46112484729
Circumradius: R = 8.69770703648

Vertex coordinates: A[17.39441407296; 0] B[0; 0] C[11.29549604568; 8.3]
Centroid: CG[9.56330337288; 2.76766666667]
Coordinates of the circumscribed circle: U[8.69770703648; 0]
Coordinates of the inscribed circle: I[10.55553892024; 3.46112484729]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.3109971114° = 126°18'36″ = 0.93770677795 rad
∠ B' = β' = 143.6990028886° = 143°41'24″ = 0.63437285472 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus b and height h

b = 10.3 ; ; h = 8.3 ; ;

2. From height h and cathetus b we calculate hypotenuse c - Euclid's theorem:

c_1**2 = b**2 - h**2 ; ; c_1 = sqrt{ 10.3**2 - 8.3**2 } = 6.099 ; ; ; ; c_1 c_2 = h**2 ; ; c_2 = h**2/c_1 = 8.3**2 / 6.099 = 11.295 ; ; ; ; c = c_1 + c_2 = 6.099 + 11.295 = 17.394 ; ;

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

c**2 = a**2+b**2 ; ; a = sqrt{ c**2 - b**2 } = sqrt{ 17.394**2 - 10.3**2 } = 14.017 ; ;
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 = 14.02 ; ; b = 10.3 ; ; c = 17.39 ; ;

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

p = a+b+c = 14.02+10.3+17.39 = 41.71 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41.71 }{ 2 } = 20.86 ; ;

6. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 14.02 * 10.3 }{ 2 } = 72.19 ; ;

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

h _a = b = 10.3 ; ; h _b = a = 14.02 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 72.19 }{ 17.39 } = 8.3 ; ;

8. 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{ 14.02 }{ 17.39 } ) = 53° 41'24" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 10.3 }{ 17.39 } ) = 36° 18'36" ; ; gamma = 90° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 72.19 }{ 20.86 } = 3.46 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14.02 }{ 2 * sin 53° 41'24" } = 8.7 ; ;

11. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.3**2+2 * 17.39**2 - 14.02**2 } }{ 2 } = 12.458 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 17.39**2+2 * 14.02**2 - 10.3**2 } }{ 2 } = 14.933 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.3**2+2 * 14.02**2 - 17.39**2 } }{ 2 } = 8.697 ; ;
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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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