Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 35   b = 33   c = 3.98

Area: T = 58.39765179441
Perimeter: p = 71.98
Semiperimeter: s = 35.99

Angle ∠ A = α = 117.2221857038° = 117°13'19″ = 2.04659073606 rad
Angle ∠ B = β = 56.97545023943° = 56°58'28″ = 0.99443926565 rad
Angle ∠ C = γ = 5.80436405676° = 5°48'13″ = 0.10112926365 rad

Height: ha = 3.33769438825
Height: hb = 3.53991829057
Height: hc = 29.34549838915

Median: ma = 15.6989811981
Median: mb = 18.65993193874
Median: mc = 33.95664412152

Inradius: r = 1.62325762141
Circumradius: R = 19.68796836603

Vertex coordinates: A[3.98; 0] B[0; 0] C[19.07554271357; 29.34549838915]
Centroid: CG[7.68551423786; 9.78216612972]
Coordinates of the circumscribed circle: U[1.99; 19.57988112246]
Coordinates of the inscribed circle: I[2.99; 1.62325762141]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 62.77881429619° = 62°46'41″ = 2.04659073606 rad
∠ B' = β' = 123.0255497606° = 123°1'32″ = 0.99443926565 rad
∠ C' = γ' = 174.1966359432° = 174°11'47″ = 0.10112926365 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 = 35+33+3.98 = 71.98 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71.98 }{ 2 } = 35.99 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.99 * (35.99-35)(35.99-33)(35.99-3.98) } ; ; T = sqrt{ 3410.15 } = 58.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 58.4 }{ 35 } = 3.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 58.4 }{ 33 } = 3.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 58.4 }{ 3.98 } = 29.34 ; ;

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{ 33**2+3.98**2-35**2 }{ 2 * 33 * 3.98 } ) = 117° 13'19" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 35**2+3.98**2-33**2 }{ 2 * 35 * 3.98 } ) = 56° 58'28" ; ; gamma = 180° - alpha - beta = 180° - 117° 13'19" - 56° 58'28" = 5° 48'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 58.4 }{ 35.99 } = 1.62 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 35 }{ 2 * sin 117° 13'19" } = 19.68 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 33**2+2 * 3.98**2 - 35**2 } }{ 2 } = 15.69 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.98**2+2 * 35**2 - 33**2 } }{ 2 } = 18.659 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 33**2+2 * 35**2 - 3.98**2 } }{ 2 } = 33.956 ; ;
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