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 = 61   b = 39   c = 72.40216574396

Area: T = 1189.5
Perimeter: p = 172.402165744
Semiperimeter: s = 86.20108287198

Angle ∠ A = α = 57.40774185274° = 57°24'27″ = 1.00219484684 rad
Angle ∠ B = β = 32.59325814726° = 32°35'33″ = 0.56988478584 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 39
Height: hb = 61
Height: hc = 32.85883638018

Median: ma = 49.51100999797
Median: mb = 64.04110024906
Median: mc = 36.20108287198

Inradius: r = 13.79991712802
Circumradius: R = 36.20108287198

Vertex coordinates: A[72.40216574396; 0] B[0; 0] C[51.39438510745; 32.85883638018]
Centroid: CG[41.26551695047; 10.95327879339]
Coordinates of the circumscribed circle: U[36.20108287198; -0]
Coordinates of the inscribed circle: I[47.20108287198; 13.79991712802]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.5932581473° = 122°35'33″ = 1.00219484684 rad
∠ B' = β' = 147.4077418527° = 147°24'27″ = 0.56988478584 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 = 61 ; ; b = 39 ; ;

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{ 61**2 + 39**2 } = 72.402 ; ;
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 = 61 ; ; b = 39 ; ; c = 72.4 ; ;

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

p = a+b+c = 61+39+72.4 = 172.4 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 172.4 }{ 2 } = 86.2 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 61 * 39 }{ 2 } = 1189.5 ; ;

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

h _a = b = 39 ; ; h _b = a = 61 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1189.5 }{ 72.4 } = 32.86 ; ;

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{ 61 }{ 72.4 } ) = 57° 24'27" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 39 }{ 72.4 } ) = 32° 35'33" ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1189.5 }{ 86.2 } = 13.8 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 61 }{ 2 * sin 57° 24'27" } = 36.2 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 39**2+2 * 72.4**2 - 61**2 } }{ 2 } = 49.51 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 72.4**2+2 * 61**2 - 39**2 } }{ 2 } = 64.041 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 39**2+2 * 61**2 - 72.4**2 } }{ 2 } = 36.201 ; ;
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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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