Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 4   b = 22   c = 24

Area: T = 39.6866269666
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 8.64658643504° = 8°38'45″ = 0.15108987996 rad
Angle ∠ B = β = 55.77111336722° = 55°46'16″ = 0.97333899101 rad
Angle ∠ C = γ = 115.5833001977° = 115°34'59″ = 2.01773039438 rad

Height: ha = 19.8433134833
Height: hb = 3.60878426969
Height: hc = 3.30771891388

Median: ma = 22.93546898824
Median: mb = 13.22987565553
Median: mc = 10.2965630141

Inradius: r = 1.58774507866
Circumradius: R = 13.30443494499

Vertex coordinates: A[24; 0] B[0; 0] C[2.25; 3.30771891388]
Centroid: CG[8.75; 1.10223963796]
Coordinates of the circumscribed circle: U[12; -5.74550599897]
Coordinates of the inscribed circle: I[3; 1.58774507866]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.354413565° = 171°21'15″ = 0.15108987996 rad
∠ B' = β' = 124.2298866328° = 124°13'44″ = 0.97333899101 rad
∠ C' = γ' = 64.41769980226° = 64°25'1″ = 2.01773039438 rad

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How did we calculate this triangle?

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

p = a+b+c = 4+22+24 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-4)(25-22)(25-24) } ; ; T = sqrt{ 1575 } = 39.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 39.69 }{ 4 } = 19.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 39.69 }{ 22 } = 3.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 39.69 }{ 24 } = 3.31 ; ;

5. 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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 22**2+24**2-4**2 }{ 2 * 22 * 24 } ) = 8° 38'45" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4**2+24**2-22**2 }{ 2 * 4 * 24 } ) = 55° 46'16" ; ; gamma = 180° - alpha - beta = 180° - 8° 38'45" - 55° 46'16" = 115° 34'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 39.69 }{ 25 } = 1.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4 }{ 2 * sin 8° 38'45" } = 13.3 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 24**2 - 4**2 } }{ 2 } = 22.935 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 4**2 - 22**2 } }{ 2 } = 13.229 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 4**2 - 24**2 } }{ 2 } = 10.296 ; ;
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