Right triangle calculator (a,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 a and hypotenuse c.

Right scalene triangle.

Sides: a = 18   b = 27.65986333719   c = 33

Area: T = 248.9287700347
Perimeter: p = 78.65986333719
Semiperimeter: s = 39.32993166859

Angle ∠ A = α = 33.05657311509° = 33°3'21″ = 0.57769313452 rad
Angle ∠ B = β = 56.94442688491° = 56°56'39″ = 0.99438649816 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 27.65986333719
Height: hb = 18
Height: hc = 15.08765272938

Median: ma = 29.08660791445
Median: mb = 22.69991189256
Median: mc = 16.5

Inradius: r = 6.32993166859
Circumradius: R = 16.5

Vertex coordinates: A[33; 0] B[0; 0] C[9.81881818182; 15.08765272938]
Centroid: CG[14.27327272727; 5.02988424313]
Coordinates of the circumscribed circle: U[16.5; 0]
Coordinates of the inscribed circle: I[11.67106833141; 6.32993166859]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.9444268849° = 146°56'39″ = 0.57769313452 rad
∠ B' = β' = 123.0565731151° = 123°3'21″ = 0.99438649816 rad
∠ C' = γ' = 90° = 1.57107963268 rad

Calculate another triangle




How did we calculate this triangle?

1. Input data entered: cathetus a and hypotenuse c

a = 18 ; ; c = 33 ; ;

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

c**2 = a**2+b**2 ; ; b = sqrt{ c**2 - a**2 } = sqrt{ 33**2 - 18**2 } = 27.659 ; ;


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 = 18 ; ; b = 27.66 ; ; c = 33 ; ;

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

p = a+b+c = 18+27.66+33 = 78.66 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 78.66 }{ 2 } = 39.33 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 18 * 27.66 }{ 2 } = 248.93 ; ;

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

h _a = b = 27.66 ; ; h _b = a = 18 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 248.93 }{ 33 } = 15.09 ; ;

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{ 18 }{ 33 } ) = 33° 3'21" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 27.66 }{ 33 } ) = 56° 56'39" ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 248.93 }{ 39.33 } = 6.33 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 18 }{ 2 * sin 33° 3'21" } = 16.5 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 27.66**2+2 * 33**2 - 18**2 } }{ 2 } = 29.086 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 33**2+2 * 18**2 - 27.66**2 } }{ 2 } = 22.699 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 27.66**2+2 * 18**2 - 33**2 } }{ 2 } = 16.5 ; ;
Calculate another triangle

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.

Calculate right triangle by:

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.