Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 16.55   b = 19.03   c = 7.21

Area: T = 58.97702920612
Perimeter: p = 42.79
Semiperimeter: s = 21.395

Angle ∠ A = α = 59.27701058288° = 59°16'12″ = 1.03444584947 rad
Angle ∠ B = β = 98.73878308876° = 98°44'16″ = 1.72333002453 rad
Angle ∠ C = γ = 21.99220632836° = 21°59'31″ = 0.38438339136 rad

Height: ha = 7.12663192823
Height: hb = 6.19876134589
Height: hc = 16.3587917354

Median: ma = 11.77222926824
Median: mb = 8.50992934489
Median: mc = 17.46549842542

Inradius: r = 2.75662651115
Circumradius: R = 9.6276729772

Vertex coordinates: A[7.21; 0] B[0; 0] C[-2.51441678225; 16.3587917354]
Centroid: CG[1.56552773925; 5.4532639118]
Coordinates of the circumscribed circle: U[3.605; 8.92662478737]
Coordinates of the inscribed circle: I[2.365; 2.75662651115]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120.7329894171° = 120°43'48″ = 1.03444584947 rad
∠ B' = β' = 81.26221691124° = 81°15'44″ = 1.72333002453 rad
∠ C' = γ' = 158.0087936716° = 158°29″ = 0.38438339136 rad

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How did we calculate this triangle?

a = 16.55 ; ; b = 19.03 ; ; c = 7.21 ; ;

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

p = a+b+c = 16.55+19.03+7.21 = 42.79 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42.79 }{ 2 } = 21.4 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.4 * (21.4-16.55)(21.4-19.03)(21.4-7.21) } ; ; T = sqrt{ 3477.5 } = 58.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 58.97 }{ 16.55 } = 7.13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 58.97 }{ 19.03 } = 6.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 58.97 }{ 7.21 } = 16.36 ; ;

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{ 19.03**2+7.21**2-16.55**2 }{ 2 * 19.03 * 7.21 } ) = 59° 16'12" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 16.55**2+7.21**2-19.03**2 }{ 2 * 16.55 * 7.21 } ) = 98° 44'16" ; ; gamma = 180° - alpha - beta = 180° - 59° 16'12" - 98° 44'16" = 21° 59'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 58.97 }{ 21.4 } = 2.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 16.55 }{ 2 * sin 59° 16'12" } = 9.63 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 19.03**2+2 * 7.21**2 - 16.55**2 } }{ 2 } = 11.772 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.21**2+2 * 16.55**2 - 19.03**2 } }{ 2 } = 8.509 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 19.03**2+2 * 16.55**2 - 7.21**2 } }{ 2 } = 17.465 ; ;
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