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 Pythagorean triangle.

Sides: a = 60   b = 80   c = 100

Area: T = 2400
Perimeter: p = 240
Semiperimeter: s = 120

Angle ∠ A = α = 36.87698976458° = 36°52'12″ = 0.64435011088 rad
Angle ∠ B = β = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 80
Height: hb = 60
Height: hc = 48

Median: ma = 85.44400374532
Median: mb = 72.11110255093
Median: mc = 50

Inradius: r = 20
Circumradius: R = 50

Vertex coordinates: A[100; 0] B[0; 0] C[36; 48]
Centroid: CG[45.33333333333; 16]
Coordinates of the circumscribed circle: U[50; 0]
Coordinates of the inscribed circle: I[40; 20]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1330102354° = 143°7'48″ = 0.64435011088 rad
∠ B' = β' = 126.8769897646° = 126°52'12″ = 0.9277295218 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 = 60 ; ; b = 80 ; ; c = 100 ; ;


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 = 80 ; ; c = 100 ; ; : Nr. 1

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

p = a+b+c = 60+80+100 = 240 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 240 }{ 2 } = 120 ; ;

4. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 60 * 80 }{ 2 } = 2400 ; ;

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

h _a = b = 80 ; ; h _b = a = 60 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2400 }{ 100 } = 48 ; ;

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{ 60 }{ 100 } ) = 36° 52'12" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 80 }{ 100 } ) = 53° 7'48" ; ; gamma = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2400 }{ 120 } = 20 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 60 }{ 2 * sin 36° 52'12" } = 50 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 80**2+2 * 100**2 - 60**2 } }{ 2 } = 85.44 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 60**2 - 80**2 } }{ 2 } = 72.111 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 80**2+2 * 60**2 - 100**2 } }{ 2 } = 50 ; ;
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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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