Right triangle calculator (a,b) - result

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 = 30   b = 12.5   c = 32.5

Area: T = 187.5
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 67.3880135052° = 67°22'49″ = 1.17660052071 rad
Angle ∠ B = β = 22.6219864948° = 22°37'11″ = 0.39547911197 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 12.5
Height: hb = 30
Height: hc = 11.53884615385

Median: ma = 19.52656241898
Median: mb = 30.64441266803
Median: mc = 16.25

Inradius: r = 5
Circumradius: R = 16.25

Vertex coordinates: A[32.5; 0] B[0; 0] C[27.69223076923; 11.53884615385]
Centroid: CG[20.06441025641; 3.84661538462]
Coordinates of the circumscribed circle: U[16.25; 0]
Coordinates of the inscribed circle: I[25; 5]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.6219864948° = 112°37'11″ = 1.17660052071 rad
∠ B' = β' = 157.3880135052° = 157°22'49″ = 0.39547911197 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 = 30 ; ; b = 12.5 ; ;

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{ 30**2 + 12.5**2 } = sqrt{ 1056.25 } = 32.5 ; ;
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 = 30 ; ; b = 12.5 ; ; c = 32.5 ; ;

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

p = a+b+c = 30+12.5+32.5 = 75 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 75 }{ 2 } = 37.5 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 30 * 12.5 }{ 2 } = 187.5 ; ;

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

h _a = b = 12.5 ; ; h _b = a = 30 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 187.5 }{ 32.5 } = 11.54 ; ;

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{ 30 }{ 32.5 } ) = 67° 22'49" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 12.5 }{ 32.5 } ) = 22° 37'11" ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 187.5 }{ 37.5 } = 5 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 30 }{ 2 * sin 67° 22'49" } = 16.25 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.5**2+2 * 32.5**2 - 30**2 } }{ 2 } = 19.526 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 32.5**2+2 * 30**2 - 12.5**2 } }{ 2 } = 30.644 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.5**2+2 * 30**2 - 32.5**2 } }{ 2 } = 16.25 ; ;
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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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