Right triangle calculator (a,b,c)

Please enter two properties of the right triangle

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


You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 4.8   b = 10.1   c = 11.55

Area: T = 24.15498930429
Perimeter: p = 26.45
Semiperimeter: s = 13.225

Angle ∠ A = α = 24.45988482092° = 24°27'32″ = 0.42768874325 rad
Angle ∠ B = β = 60.59993524269° = 60°35'58″ = 1.05876582244 rad
Angle ∠ C = γ = 94.94217993639° = 94°56'30″ = 1.65770469967 rad

Height: ha = 10.06224554345
Height: hb = 4.78221570382
Height: hc = 4.18217996611

Median: ma = 10.58804654907
Median: mb = 7.26107678657
Median: mc = 5.40113308545

Inradius: r = 1.8266078869
Circumradius: R = 5.79765474113

Vertex coordinates: A[11.55; 0] B[0; 0] C[2.35663852814; 4.18217996611]
Centroid: CG[4.63554617605; 1.39439332204]
Coordinates of the circumscribed circle: U[5.775; -0.49993364506]
Coordinates of the inscribed circle: I[3.125; 1.8266078869]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.5411151791° = 155°32'28″ = 0.42768874325 rad
∠ B' = β' = 119.4010647573° = 119°24'2″ = 1.05876582244 rad
∠ C' = γ' = 85.05882006361° = 85°3'30″ = 1.65770469967 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c

a = 4.8 ; ; b = 10.1 ; ; c = 11.55 ; ;


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 = 4.8 ; ; b = 10.1 ; ; c = 11.55 ; ; : Nr. 1

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

p = a+b+c = 4.8+10.1+11.55 = 26.45 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 26.45 }{ 2 } = 13.23 ; ;

4. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 4.8 * 10.1 }{ 2 } = 24.15 ; ;

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

h _a = b = 10.06 ; ; h _b = a = 4.78 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 24.15 }{ 11.55 } = 4.18 ; ;

6. 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{ 4.8 }{ 11.55 } ) = 24° 27'32" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 10.1 }{ 11.55 } ) = 60° 35'58" ; ; gamma = 94° 56'30" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 24.15 }{ 13.23 } = 1.83 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4.8 }{ 2 * sin 24° 27'32" } = 5.8 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.1**2+2 * 11.55**2 - 4.8**2 } }{ 2 } = 10.58 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.55**2+2 * 4.8**2 - 10.1**2 } }{ 2 } = 7.261 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.1**2+2 * 4.8**2 - 11.55**2 } }{ 2 } = 5.401 ; ;
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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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