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 = 7.81545750947   b = 13.8   c = 15.85989906334

Area: T = 53.92105681537
Perimeter: p = 37.47435657282
Semiperimeter: s = 18.73767828641

Angle ∠ A = α = 29.5221730485° = 29°31'18″ = 0.51552513978 rad
Angle ∠ B = β = 60.4788269515° = 60°28'42″ = 1.05655449289 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 13.8
Height: hb = 7.81545750947
Height: hc = 6.8

Median: ma = 14.34224856973
Median: mb = 10.42548541434
Median: mc = 7.92994953167

Inradius: r = 2.87877922307
Circumradius: R = 7.92994953167

Vertex coordinates: A[15.85989906334; 0] B[0; 0] C[3.85106601916; 6.8]
Centroid: CG[6.57698836083; 2.26766666667]
Coordinates of the circumscribed circle: U[7.92994953167; 0]
Coordinates of the inscribed circle: I[4.93767828641; 2.87877922307]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.4788269515° = 150°28'42″ = 0.51552513978 rad
∠ B' = β' = 119.5221730485° = 119°31'18″ = 1.05655449289 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 = 13.8 ; ; h = 6.8 ; ;

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

c_1**2 = b**2 - h**2 ; ; c_1 = sqrt{ 13.8**2 - 6.8**2 } = 12.008 ; ; ; ; c_1 c_2 = h**2 ; ; c_2 = h**2/c_1 = 6.8**2 / 12.008 = 3.851 ; ; ; ; c = c_1 + c_2 = 12.008 + 3.851 = 15.859 ; ;

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{ 15.859**2 - 13.8**2 } = 7.815 ; ;


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 = 7.81 ; ; b = 13.8 ; ; c = 15.86 ; ;

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

p = a+b+c = 7.81+13.8+15.86 = 37.47 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37.47 }{ 2 } = 18.74 ; ;

6. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 7.81 * 13.8 }{ 2 } = 53.92 ; ;

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

h _a = b = 13.8 ; ; h _b = a = 7.81 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 53.92 }{ 15.86 } = 6.8 ; ;

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{ 7.81 }{ 15.86 } ) = 29° 31'18" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 13.8 }{ 15.86 } ) = 60° 28'42" ; ; gamma = 90° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 53.92 }{ 18.74 } = 2.88 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.81 }{ 2 * sin 29° 31'18" } = 7.93 ; ;

11. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.8**2+2 * 15.86**2 - 7.81**2 } }{ 2 } = 14.342 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.86**2+2 * 7.81**2 - 13.8**2 } }{ 2 } = 10.425 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.8**2+2 * 7.81**2 - 15.86**2 } }{ 2 } = 7.929 ; ;
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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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