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 = 60   b = 91   c = 109

Area: T = 2730
Perimeter: p = 260
Semiperimeter: s = 130

Angle ∠ A = α = 33.3988488468° = 33°23'55″ = 0.5832913589 rad
Angle ∠ B = β = 56.6021511532° = 56°36'5″ = 0.98878827378 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 91
Height: hb = 60
Height: hc = 50.09217431193

Median: ma = 95.81875349297
Median: mb = 75.30110624095
Median: mc = 54.5

Inradius: r = 21
Circumradius: R = 54.5

Vertex coordinates: A[109; 0] B[0; 0] C[33.02875229358; 50.09217431193]
Centroid: CG[47.34325076453; 16.69772477064]
Coordinates of the circumscribed circle: U[54.5; -0]
Coordinates of the inscribed circle: I[39; 21]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.6021511532° = 146°36'5″ = 0.5832913589 rad
∠ B' = β' = 123.3988488468° = 123°23'55″ = 0.98878827378 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 = 60 ; ; c = 109 ; ;

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{ 109**2 - 60**2 } = 91 ; ;
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 = 60 ; ; b = 91 ; ; c = 109 ; ;

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

p = a+b+c = 60+91+109 = 260 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 260 }{ 2 } = 130 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 60 * 91 }{ 2 } = 2730 ; ;

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

h _a = b = 91 ; ; h _b = a = 60 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2730 }{ 109 } = 50.09 ; ;

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{ 60 }{ 109 } ) = 33° 23'55" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 91 }{ 109 } ) = 56° 36'5" ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2730 }{ 130 } = 21 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 60 }{ 2 * sin 33° 23'55" } = 54.5 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 91**2+2 * 109**2 - 60**2 } }{ 2 } = 95.818 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 109**2+2 * 60**2 - 91**2 } }{ 2 } = 75.301 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 91**2+2 * 60**2 - 109**2 } }{ 2 } = 54.5 ; ;
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.