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 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 using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.23 * (13.23-4.8)(13.23-10.1)(13.23-11.55) } ; ; T = sqrt{ 583.22 } = 24.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 24.15 }{ 4.8 } = 10.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 24.15 }{ 10.1 } = 4.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 24.15 }{ 11.55 } = 4.18 ; ;

6. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 4.8**2-10.1**2-11.55**2 }{ 2 * 10.1 * 11.55 } ) = 24° 27'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10.1**2-4.8**2-11.55**2 }{ 2 * 4.8 * 11.55 } ) = 60° 35'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11.55**2-4.8**2-10.1**2 }{ 2 * 10.1 * 4.8 } ) = 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 ; ;
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