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 = 1750   b = 1477   c = 2289.984449776

Area: T = 1292375
Perimeter: p = 5516.984449776
Semiperimeter: s = 2758.492224888

Angle ∠ A = α = 49.83656341958° = 49°50'8″ = 0.87697959015 rad
Angle ∠ B = β = 40.16443658042° = 40°9'52″ = 0.70110004253 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 1477
Height: hb = 1750
Height: hc = 1128.71994313

Median: ma = 1716.728770118
Median: mb = 1899.443261561
Median: mc = 1144.992224888

Inradius: r = 468.5087751118
Circumradius: R = 1144.992224888

Vertex coordinates: A[2289.984449776; 0] B[0; 0] C[1337.345529775; 1128.71994313]
Centroid: CG[1209.110993184; 376.2439810433]
Coordinates of the circumscribed circle: U[1144.992224888; 0]
Coordinates of the inscribed circle: I[1281.492224888; 468.5087751118]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.1644365804° = 130°9'52″ = 0.87697959015 rad
∠ B' = β' = 139.8365634196° = 139°50'8″ = 0.70110004253 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus a and cathetus b

a = 1750 ; ; b = 1477 ; ;

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{ 1750**2 + 1477**2 } = sqrt{ 5244029 } = 2289.984 ; ;
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 = 1750 ; ; b = 1477 ; ; c = 2289.98 ; ;

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

p = a+b+c = 1750+1477+2289.98 = 5516.98 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 5516.98 }{ 2 } = 2758.49 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 1750 * 1477 }{ 2 } = 1292375 ; ;

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

h _a = b = 1477 ; ; h _b = a = 1750 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1292375 }{ 2289.98 } = 1128.72 ; ;

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{ 1750 }{ 2289.98 } ) = 49° 50'8" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 1477 }{ 2289.98 } ) = 40° 9'52" ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1292375 }{ 2758.49 } = 468.51 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1750 }{ 2 * sin 49° 50'8" } = 1144.99 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1477**2+2 * 2289.98**2 - 1750**2 } }{ 2 } = 1716.728 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2289.98**2+2 * 1750**2 - 1477**2 } }{ 2 } = 1899.443 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1477**2+2 * 1750**2 - 2289.98**2 } }{ 2 } = 1144.992 ; ;
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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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