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 = 2.4   b = 100   c = 100.0298795854

Area: T = 120
Perimeter: p = 202.4298795854
Semiperimeter: s = 101.2144397927

Angle ∠ A = α = 1.37548347806° = 1°22'29″ = 0.02439953936 rad
Angle ∠ B = β = 88.62551652194° = 88°37'31″ = 1.54768009332 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 100
Height: hb = 2.4
Height: hc = 2.39993090985

Median: ma = 100.0077199741
Median: mb = 50.05875668606
Median: mc = 50.0144397927

Inradius: r = 1.1865602073
Circumradius: R = 50.0144397927

Vertex coordinates: A[100.0298795854; 0] B[0; 0] C[0.05875834184; 2.39993090985]
Centroid: CG[33.36221264241; 0.87997696995]
Coordinates of the circumscribed circle: U[50.0144397927; -0]
Coordinates of the inscribed circle: I[1.2144397927; 1.1865602073]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 178.6255165219° = 178°37'31″ = 0.02439953936 rad
∠ B' = β' = 91.37548347806° = 91°22'29″ = 1.54768009332 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 = 2.4 ; ; b = 100 ; ;

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{ 2.4**2 + 100**2 } = sqrt{ 10005.76 } = 100.029 ; ;
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 = 2.4 ; ; b = 100 ; ; c = 100.03 ; ;

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

p = a+b+c = 2.4+100+100.03 = 202.43 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 202.43 }{ 2 } = 101.21 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 2.4 * 100 }{ 2 } = 120 ; ;

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

h _a = b = 100 ; ; h _b = a = 2.4 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 120 }{ 100.03 } = 2.4 ; ;

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{ 2.4 }{ 100.03 } ) = 1° 22'29" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 100 }{ 100.03 } ) = 88° 37'31" ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 120 }{ 101.21 } = 1.19 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.4 }{ 2 * sin 1° 22'29" } = 50.01 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 100.03**2 - 2.4**2 } }{ 2 } = 100.007 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 100.03**2+2 * 2.4**2 - 100**2 } }{ 2 } = 50.058 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 2.4**2 - 100.03**2 } }{ 2 } = 50.014 ; ;
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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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