Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 49   b = 43   c = 86.26

Area: T = 688.1443811809
Perimeter: p = 178.26
Semiperimeter: s = 89.13

Angle ∠ A = α = 21.78803279402° = 21°46'49″ = 0.38801384347 rad
Angle ∠ B = β = 19.00328054502° = 19°10″ = 0.33216615222 rad
Angle ∠ C = γ = 139.217686661° = 139°13'1″ = 2.43297926966 rad

Height: ha = 28.08875025228
Height: hb = 32.00766889213
Height: hc = 15.95551080874

Median: ma = 63.59875141024
Median: mb = 66.77330769098
Median: mc = 16.27327717369

Inradius: r = 7.72106755504
Circumradius: R = 66.02990105357

Vertex coordinates: A[86.26; 0] B[0; 0] C[46.33296290285; 15.95551080874]
Centroid: CG[44.19765430095; 5.31883693625]
Coordinates of the circumscribed circle: U[43.13; -49.99663331888]
Coordinates of the inscribed circle: I[46.13; 7.72106755504]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.221967206° = 158°13'11″ = 0.38801384347 rad
∠ B' = β' = 160.997719455° = 160°59'50″ = 0.33216615222 rad
∠ C' = γ' = 40.78331333904° = 40°46'59″ = 2.43297926966 rad

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How did we calculate this triangle?

a = 49 ; ; b = 43 ; ; c = 86.26 ; ;

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

p = a+b+c = 49+43+86.26 = 178.26 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 178.26 }{ 2 } = 89.13 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 89.13 * (89.13-49)(89.13-43)(89.13-86.26) } ; ; T = sqrt{ 473541.91 } = 688.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 688.14 }{ 49 } = 28.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 688.14 }{ 43 } = 32.01 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 688.14 }{ 86.26 } = 15.96 ; ;

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{ 43**2+86.26**2-49**2 }{ 2 * 43 * 86.26 } ) = 21° 46'49" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 49**2+86.26**2-43**2 }{ 2 * 49 * 86.26 } ) = 19° 10" ; ; gamma = 180° - alpha - beta = 180° - 21° 46'49" - 19° 10" = 139° 13'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 688.14 }{ 89.13 } = 7.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 49 }{ 2 * sin 21° 46'49" } = 66.03 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 43**2+2 * 86.26**2 - 49**2 } }{ 2 } = 63.598 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 86.26**2+2 * 49**2 - 43**2 } }{ 2 } = 66.773 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 43**2+2 * 49**2 - 86.26**2 } }{ 2 } = 16.273 ; ;
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