Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 22.42   b = 16.8   c = 35.34

Area: T = 148.3598760985
Perimeter: p = 74.56
Semiperimeter: s = 37.28

Angle ∠ A = α = 29.98545700935° = 29°59'4″ = 0.52333294729 rad
Angle ∠ B = β = 21.99328386443° = 21°59'34″ = 0.38438474462 rad
Angle ∠ C = γ = 128.0232591262° = 128°1'21″ = 2.23444157345 rad

Height: ha = 13.23545014259
Height: hb = 17.66217572601
Height: hc = 8.39660815498

Median: ma = 25.29765155703
Median: mb = 28.37765043654
Median: mc = 8.95765227628

Inradius: r = 3.98795804985
Circumradius: R = 22.43304634112

Vertex coordinates: A[35.34; 0] B[0; 0] C[20.78985116016; 8.39660815498]
Centroid: CG[18.71095038672; 2.79986938499]
Coordinates of the circumscribed circle: U[17.67; -13.81765404078]
Coordinates of the inscribed circle: I[20.48; 3.98795804985]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0155429907° = 150°56″ = 0.52333294729 rad
∠ B' = β' = 158.0077161356° = 158°26″ = 0.38438474462 rad
∠ C' = γ' = 51.97774087378° = 51°58'39″ = 2.23444157345 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 = 22.42+16.8+35.34 = 74.56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74.56 }{ 2 } = 37.28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.28 * (37.28-22.42)(37.28-16.8)(37.28-35.34) } ; ; T = sqrt{ 22010.32 } = 148.36 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 148.36 }{ 22.42 } = 13.23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 148.36 }{ 16.8 } = 17.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 148.36 }{ 35.34 } = 8.4 ; ;

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{ 16.8**2+35.34**2-22.42**2 }{ 2 * 16.8 * 35.34 } ) = 29° 59'4" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 22.42**2+35.34**2-16.8**2 }{ 2 * 22.42 * 35.34 } ) = 21° 59'34" ; ;
 gamma = 180° - alpha - beta = 180° - 29° 59'4" - 21° 59'34" = 128° 1'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 148.36 }{ 37.28 } = 3.98 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 22.42 }{ 2 * sin 29° 59'4" } = 22.43 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.8**2+2 * 35.34**2 - 22.42**2 } }{ 2 } = 25.297 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 35.34**2+2 * 22.42**2 - 16.8**2 } }{ 2 } = 28.377 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.8**2+2 * 22.42**2 - 35.34**2 } }{ 2 } = 8.957 ; ;
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