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 = 140   b = 140   c = 197.9989898732

Area: T = 9800
Perimeter: p = 477.9989898732
Semiperimeter: s = 238.9954949366

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

Height: ha = 140
Height: hb = 140
Height: hc = 98.99549493661

Median: ma = 156.5254758425
Median: mb = 156.5254758425
Median: mc = 98.99549493661

Inradius: r = 41.00550506339
Circumradius: R = 98.99549493661

Vertex coordinates: A[197.9989898732; 0] B[0; 0] C[98.99549493661; 98.99549493661]
Centroid: CG[98.99549493661; 32.99883164554]
Coordinates of the circumscribed circle: U[98.99549493661; 0]
Coordinates of the inscribed circle: I[98.99549493661; 41.00550506339]

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 = 140 ; ; 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{ 140**2 + 140**2 } = 197.99 ; ;
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 = 140 ; ; b = 140 ; ; c = 197.99 ; ;

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

p = a+b+c = 140+140+197.99 = 477.99 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 477.99 }{ 2 } = 238.99 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 140 * 140 }{ 2 } = 9800 ; ;

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

h _a = b = 140 ; ; h _b = a = 140 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9800 }{ 197.99 } = 98.99 ; ;

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{ 140 }{ 197.99 } ) = 45° ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 140 }{ 197.99 } ) = 45° ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9800 }{ 238.99 } = 41.01 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 140 }{ 2 * sin 45° } = 98.99 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 140**2+2 * 197.99**2 - 140**2 } }{ 2 } = 156.525 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 197.99**2+2 * 140**2 - 140**2 } }{ 2 } = 156.525 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 140**2+2 * 140**2 - 197.99**2 } }{ 2 } = 98.995 ; ;
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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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