Right triangle calculator (a)

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 perimeter o.

Right scalene triangle.

Sides: a = 43   b = 26.49435064935   c = 50.50664935065

Area: T = 569.611038961
Perimeter: p = 120
Semiperimeter: s = 60

Angle ∠ A = α = 58.3621612105° = 58°21'42″ = 1.0198602288 rad
Angle ∠ B = β = 31.6388387895° = 31°38'18″ = 0.55221940388 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 26.49435064935
Height: hb = 43
Height: hc = 22.55659269735

Median: ma = 34.12197286965
Median: mb = 44.99441826415
Median: mc = 25.25332467532

Inradius: r = 9.49435064935
Circumradius: R = 25.25332467532

Vertex coordinates: A[50.50664935065; 0] B[0; 0] C[36.60991540242; 22.55659269735]
Centroid: CG[29.03985491769; 7.51986423245]
Coordinates of the circumscribed circle: U[25.25332467532; 0]
Coordinates of the inscribed circle: I[33.50664935065; 9.49435064935]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.6388387895° = 121°38'18″ = 1.0198602288 rad
∠ B' = β' = 148.3621612105° = 148°21'42″ = 0.55221940388 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus a and perimeter o

a = 43 ; ; o = 120 ; ;

2. From cathetus a and perimeter o we calculate cathetus b:

k_1 = p - a = b + c = 120-43 = 77 ; ; b = fraction{ k_1**2 - a**2 }{ 2 * k_1 } ; ; b = fraction{ 77**2 - 1849 }{ 2 * 77 } = 26.494 ; ;

3. From cathetus a we calculate hypotenuse c - Pythagorean theorem:

c**2 = a**2+b**2 ; ; c = sqrt{ a**2+b**2 } = sqrt{ 43**2 + 26.494**2 } = sqrt{ 2550.906 } = 50.506 ; ;
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 = 43 ; ; b = 26.49 ; ; c = 50.51 ; ;

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

p = a+b+c = 43+26.49+50.51 = 120 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 120 }{ 2 } = 60 ; ;

6. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 43 * 26.49 }{ 2 } = 569.61 ; ;

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

h _a = b = 26.49 ; ; h _b = a = 43 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 569.61 }{ 50.51 } = 22.56 ; ;

8. 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{ 43 }{ 50.51 } ) = 58° 21'42" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 26.49 }{ 50.51 } ) = 31° 38'18" ; ; gamma = 90° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 569.61 }{ 60 } = 9.49 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 43 }{ 2 * sin 58° 21'42" } = 25.25 ; ;

11. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 26.49**2+2 * 50.51**2 - 43**2 } }{ 2 } = 34.12 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 50.51**2+2 * 43**2 - 26.49**2 } }{ 2 } = 44.994 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 26.49**2+2 * 43**2 - 50.51**2 } }{ 2 } = 25.253 ; ;
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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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