Right triangle calculator (a,b)

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 = 95   b = 140   c = 169.1899243157

Area: T = 6650
Perimeter: p = 404.1899243157
Semiperimeter: s = 202.0954621578

Angle ∠ A = α = 34.16596945457° = 34°9'35″ = 0.59661991413 rad
Angle ∠ B = β = 55.84403054543° = 55°50'25″ = 0.97545971855 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 140
Height: hb = 95
Height: hc = 78.61101985672

Median: ma = 147.839859442
Median: mb = 118.0044237212
Median: mc = 84.59546215784

Inradius: r = 32.90553784216
Circumradius: R = 84.59546215784

Vertex coordinates: A[169.1899243157; 0] B[0; 0] C[53.3432634742; 78.61101985672]
Centroid: CG[74.1777292633; 26.20333995224]
Coordinates of the circumscribed circle: U[84.59546215784; 0]
Coordinates of the inscribed circle: I[62.09546215784; 32.90553784216]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.8440305454° = 145°50'25″ = 0.59661991413 rad
∠ B' = β' = 124.1659694546° = 124°9'35″ = 0.97545971855 rad
∠ C' = γ' = 90° = 1.57107963268 rad

Calculate another triangle




How did we calculate this triangle?

1. Input data entered: cathetus a and cathetus b

a = 95 ; ; b = 140 ; ;

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{ 95**2 + 140**2 } = 169.189 ; ;


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 = 95 ; ; b = 140 ; ; c = 169.19 ; ;

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

p = a+b+c = 95+140+169.19 = 404.19 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 404.19 }{ 2 } = 202.09 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 95 * 140 }{ 2 } = 6650 ; ;

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

h _a = b = 140 ; ; h _b = a = 95 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6650 }{ 169.19 } = 78.61 ; ;

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{ 95 }{ 169.19 } ) = 34° 9'35" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 140 }{ 169.19 } ) = 55° 50'25" ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6650 }{ 202.09 } = 32.91 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 95 }{ 2 * sin 34° 9'35" } = 84.59 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 140**2+2 * 169.19**2 - 95**2 } }{ 2 } = 147.839 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 169.19**2+2 * 95**2 - 140**2 } }{ 2 } = 118.004 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 140**2+2 * 95**2 - 169.19**2 } }{ 2 } = 84.595 ; ;
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.