Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 189.74   b = 63.25   c = 200

Area: T = 6000.527748256
Perimeter: p = 452.99
Semiperimeter: s = 226.495

Angle ∠ A = α = 71.56880770626° = 71°34'5″ = 1.24990985841 rad
Angle ∠ B = β = 18.43662915953° = 18°26'11″ = 0.32217739902 rad
Angle ∠ C = γ = 89.99656313422° = 89°59'44″ = 1.57107200793 rad

Height: ha = 63.25499998161
Height: hb = 189.7439999448
Height: hc = 60.00552748256

Median: ma = 114.0177386174
Median: mb = 192.355512256
Median: mc = 100.0054575145

Inradius: r = 26.49329799005
Circumradius: R = 1000.000000291

Vertex coordinates: A[200; 0] B[0; 0] C[180.002176275; 60.00552748256]
Centroid: CG[126.667725425; 20.00217582752]
Coordinates of the circumscribed circle: U[100; 0.00876247463]
Coordinates of the inscribed circle: I[163.245; 26.49329799005]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 108.4321922937° = 108°25'55″ = 1.24990985841 rad
∠ B' = β' = 161.5643708405° = 161°33'49″ = 0.32217739902 rad
∠ C' = γ' = 90.00443686578° = 90°16″ = 1.57107200793 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 = 189.74+63.25+200 = 452.99 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 452.99 }{ 2 } = 226.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 226.5 * (226.5-189.74)(226.5-63.25)(226.5-200) } ; ; T = sqrt{ 36006330.07 } = 6000.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6000.53 }{ 189.74 } = 63.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6000.53 }{ 63.25 } = 189.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6000.53 }{ 200 } = 60.01 ; ;

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{ 63.25**2+200**2-189.74**2 }{ 2 * 63.25 * 200 } ) = 71° 34'5" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 189.74**2+200**2-63.25**2 }{ 2 * 189.74 * 200 } ) = 18° 26'11" ; ;
 gamma = 180° - alpha - beta = 180° - 71° 34'5" - 18° 26'11" = 89° 59'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6000.53 }{ 226.5 } = 26.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 189.74 }{ 2 * sin 71° 34'5" } = 100 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 63.25**2+2 * 200**2 - 189.74**2 } }{ 2 } = 114.017 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 200**2+2 * 189.74**2 - 63.25**2 } }{ 2 } = 192.355 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 63.25**2+2 * 189.74**2 - 200**2 } }{ 2 } = 100.005 ; ;
Calculate another triangle


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

See more information about triangles or more details on solving triangles.