Right triangle calculator (c,h) - result

Please enter two properties of the right triangle

Use symbols: a, b, c, A, B, h, T, p, r, R


You have entered hypotenuse c and height h.

Right scalene triangle.

Sides: a = 4.4722135955   b = 2.23660679775   c = 5

Area: T = 5
Perimeter: p = 11.70882039325
Semiperimeter: s = 5.85441019662

Angle ∠ A = α = 63.43549488229° = 63°26'6″ = 1.10771487178 rad
Angle ∠ B = β = 26.56550511771° = 26°33'54″ = 0.4643647609 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 2.23660679775
Height: hb = 4.4722135955
Height: hc = 2

Median: ma = 3.16222776602
Median: mb = 4.61097722286
Median: mc = 2.5

Inradius: r = 0.85441019662
Circumradius: R = 2.5

Vertex coordinates: A[5; 0] B[0; 0] C[4; 2]
Centroid: CG[3; 0.66766666667]
Coordinates of the circumscribed circle: U[2.5; 0]
Coordinates of the inscribed circle: I[3.61880339887; 0.85441019662]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.5655051177° = 116°33'54″ = 1.10771487178 rad
∠ B' = β' = 153.4354948823° = 153°26'6″ = 0.4643647609 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: hypotenuse c and height h

c = 5 ; ; h = 2 ; ;

2. From hypotenuse c and height h we calculate a,b - Pythagorean theorem, Euclid's theorem:

c = c_1+c_2 ; ; h**2 = c_1 * c_2 ; ; ; ; h**2 = c_1 * (c-c_1) ; ; h**2 = c_1 * c-c_1 **2 ; ; ; ; c_1**2 -c_1 * c + h**2 = 0 ; ; ; ; c_1**2 -5 * c_1 + 4 = 0 ; ; ; ; c_1 = 4 ; ; c_2 = 1 ; ; ; ; a = sqrt{ c_1**2+h**2 } = sqrt{ 4**2+2**2 } = 4.472 ; ; b = sqrt{ c_2**2+h**2 } = sqrt{ 1**2+2**2 } = 2.236 ; ;
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 = 4.47 ; ; b = 2.24 ; ; c = 5 ; ;

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

p = a+b+c = 4.47+2.24+5 = 11.71 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.71 }{ 2 } = 5.85 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 4.47 * 2.24 }{ 2 } = 5 ; ;

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

h _a = b = 2.24 ; ; h _b = a = 4.47 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5 }{ 5 } = 2 ; ;

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{ 4.47 }{ 5 } ) = 63° 26'6" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 2.24 }{ 5 } ) = 26° 33'54" ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5 }{ 5.85 } = 0.85 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4.47 }{ 2 * sin 63° 26'6" } = 2.5 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.24**2+2 * 5**2 - 4.47**2 } }{ 2 } = 3.162 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5**2+2 * 4.47**2 - 2.24**2 } }{ 2 } = 4.61 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.24**2+2 * 4.47**2 - 5**2 } }{ 2 } = 2.5 ; ;
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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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