Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 173.07   b = 115.38   c = 208

Area: T = 9984.40882902
Perimeter: p = 496.45
Semiperimeter: s = 248.225

Angle ∠ A = α = 56.31216897639° = 56°18'42″ = 0.98328243937 rad
Angle ∠ B = β = 33.69108485293° = 33°41'27″ = 0.58880162346 rad
Angle ∠ C = γ = 89.99774617068° = 89°59'51″ = 1.57107520252 rad

Height: ha = 115.3879999887
Height: hb = 173.076999983
Height: hc = 96.00439258673

Median: ma = 144.2221933058
Median: mb = 182.4299373594
Median: mc = 104.0044253038

Inradius: r = 40.22332180087
Circumradius: R = 1044.000000102

Vertex coordinates: A[208; 0] B[0; 0] C[144.0021635817; 96.00439258673]
Centroid: CG[117.3343878606; 32.00113086224]
Coordinates of the circumscribed circle: U[104; 0.00546073637]
Coordinates of the inscribed circle: I[132.845; 40.22332180087]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 123.6888310236° = 123°41'18″ = 0.98328243937 rad
∠ B' = β' = 146.3099151471° = 146°18'33″ = 0.58880162346 rad
∠ C' = γ' = 90.00325382932° = 90°9″ = 1.57107520252 rad

Calculate another triangle


How did we calculate this triangle?

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

p = a+b+c = 173.07+115.38+208 = 496.45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 496.45 }{ 2 } = 248.23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 248.23 * (248.23-173.07)(248.23-115.38)(248.23-208) } ; ; T = sqrt{ 99688408.91 } = 9984.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9984.41 }{ 173.07 } = 115.38 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9984.41 }{ 115.38 } = 173.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9984.41 }{ 208 } = 96 ; ;

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{ 115.38**2+208**2-173.07**2 }{ 2 * 115.38 * 208 } ) = 56° 18'42" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 173.07**2+208**2-115.38**2 }{ 2 * 173.07 * 208 } ) = 33° 41'27" ; ; gamma = 180° - alpha - beta = 180° - 56° 18'42" - 33° 41'27" = 89° 59'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9984.41 }{ 248.23 } = 40.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 173.07 }{ 2 * sin 56° 18'42" } = 104 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 115.38**2+2 * 208**2 - 173.07**2 } }{ 2 } = 144.222 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 208**2+2 * 173.07**2 - 115.38**2 } }{ 2 } = 182.429 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 115.38**2+2 * 173.07**2 - 208**2 } }{ 2 } = 104.004 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.