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 isosceles triangle.

Sides: a = 60   b = 60   c = 84.85328137424

Area: T = 1800
Perimeter: p = 204.8532813742
Semiperimeter: s = 102.4266406871

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 60
Height: hb = 60
Height: hc = 42.42664068712

Median: ma = 67.0822039325
Median: mb = 67.0822039325
Median: mc = 42.42664068712

Inradius: r = 17.57435931288
Circumradius: R = 42.42664068712

Vertex coordinates: A[84.85328137424; 0] B[0; 0] C[42.42664068712; 42.42664068712]
Centroid: CG[42.42664068712; 14.14221356237]
Coordinates of the circumscribed circle: U[42.42664068712; -0]
Coordinates of the inscribed circle: I[42.42664068712; 17.57435931288]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 135° = 0.78553981634 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 = 60 ; ; b = 60 ; ;

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{ 60**2 + 60**2 } = 84.853 ; ;


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 = 60 ; ; c = 84.85 ; ;

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

p = a+b+c = 60+60+84.85 = 204.85 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 204.85 }{ 2 } = 102.43 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 60 * 60 }{ 2 } = 1800 ; ;

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

h _a = b = 60 ; ; h _b = a = 60 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1800 }{ 84.85 } = 42.43 ; ;

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 }{ 84.85 } ) = 45° ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 60 }{ 84.85 } ) = 45° ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1800 }{ 102.43 } = 17.57 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 60 }{ 2 * sin 45° } = 42.43 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 84.85**2 - 60**2 } }{ 2 } = 67.082 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 84.85**2+2 * 60**2 - 60**2 } }{ 2 } = 67.082 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 60**2 - 84.85**2 } }{ 2 } = 42.426 ; ;
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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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