Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 16.51   b = 15.25   c = 1.44

Area: T = 5.53295753906
Perimeter: p = 33.2
Semiperimeter: s = 16.6

Angle ∠ A = α = 149.761125249° = 149°45'40″ = 2.61438269479 rad
Angle ∠ B = β = 27.72112604653° = 27°43'17″ = 0.48438272679 rad
Angle ∠ C = γ = 2.51774870444° = 2°31'3″ = 0.04439384378 rad

Height: ha = 0.67698455955
Height: hb = 0.72551902152
Height: hc = 7.68799658202

Median: ma = 7.01223480376
Median: mb = 8.89986642256
Median: mc = 15.87661739723

Inradius: r = 0.33331069512
Circumradius: R = 16.39218372746

Vertex coordinates: A[1.44; 0] B[0; 0] C[14.615; 7.68799658202]
Centroid: CG[5.35216666667; 2.56599886067]
Coordinates of the circumscribed circle: U[0.72; 16.37660168917]
Coordinates of the inscribed circle: I[1.35; 0.33331069512]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 30.23987475097° = 30°14'19″ = 2.61438269479 rad
∠ B' = β' = 152.2798739535° = 152°16'43″ = 0.48438272679 rad
∠ C' = γ' = 177.4832512956° = 177°28'57″ = 0.04439384378 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 = 16.51+15.25+1.44 = 33.2 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33.2 }{ 2 } = 16.6 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.6 * (16.6-16.51)(16.6-15.25)(16.6-1.44) } ; ; T = sqrt{ 30.58 } = 5.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5.53 }{ 16.51 } = 0.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5.53 }{ 15.25 } = 0.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5.53 }{ 1.44 } = 7.68 ; ;

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{ 15.25**2+1.44**2-16.51**2 }{ 2 * 15.25 * 1.44 } ) = 149° 45'40" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 16.51**2+1.44**2-15.25**2 }{ 2 * 16.51 * 1.44 } ) = 27° 43'17" ; ; gamma = 180° - alpha - beta = 180° - 149° 45'40" - 27° 43'17" = 2° 31'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5.53 }{ 16.6 } = 0.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 16.51 }{ 2 * sin 149° 45'40" } = 16.39 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.25**2+2 * 1.44**2 - 16.51**2 } }{ 2 } = 7.012 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.44**2+2 * 16.51**2 - 15.25**2 } }{ 2 } = 8.899 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.25**2+2 * 16.51**2 - 1.44**2 } }{ 2 } = 15.876 ; ;
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