Right triangle calculator

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, cathetus b and hypotenuse c.

Right scalene triangle.

Sides: a = 550   b = 330   c = 641.4054708433

Area: T = 90750
Perimeter: p = 1521.4054708433
Semiperimeter: s = 760.70223542165

Angle ∠ A = α = 59.03662434679° = 59°2'10″ = 1.03303768265 rad
Angle ∠ B = β = 30.96437565321° = 30°57'50″ = 0.54404195003 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 330
Height: hb = 550
Height: hc = 282.97326654851

Median: ma = 429.56437321749
Median: mb = 574.21768579901
Median: mc = 320.70223542165

Inradius: r = 119.29876457835
Circumradius: R = 320.70223542165

Vertex coordinates: A[641.4054708433; 0] B[0; 0] C[471.62111091419; 282.97326654851]
Centroid: CG[371.00986058583; 94.32442218284]
Coordinates of the circumscribed circle: U[320.70223542165; 0]
Coordinates of the inscribed circle: I[430.70223542165; 119.29876457835]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120.96437565321° = 120°57'50″ = 1.03303768265 rad
∠ B' = β' = 149.03662434679° = 149°2'10″ = 0.54404195003 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus a, cathetus b and hypotenuse c

a = 550 ; ; b = 330 ; ; c = 641.405 ; ;


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 = 550 ; ; b = 330 ; ; c = 641.4 ; ;

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

p = a+b+c = 550+330+641.4 = 1521.4 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1521.4 }{ 2 } = 760.7 ; ;

4. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 550 * 330 }{ 2 } = 90750 ; ;

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

h _a = b = 330 ; ; h _b = a = 550 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 90750 }{ 641.4 } = 282.97 ; ;

6. 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{ 550 }{ 641.4 } ) = 59° 2'10" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 330 }{ 641.4 } ) = 30° 57'50" ; ; gamma = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 90750 }{ 760.7 } = 119.3 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 550 }{ 2 * sin 59° 2'10" } = 320.7 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 330**2+2 * 641.4**2 - 550**2 } }{ 2 } = 429.564 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 641.4**2+2 * 550**2 - 330**2 } }{ 2 } = 574.217 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 330**2+2 * 550**2 - 641.4**2 } }{ 2 } = 320.702 ; ;
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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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