Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 6   b = 15   c = 18

Area: T = 42.15437364892
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 18.19548723388° = 18°11'42″ = 0.31875604293 rad
Angle ∠ B = β = 51.31878125465° = 51°19'4″ = 0.89656647939 rad
Angle ∠ C = γ = 110.4877315115° = 110°29'14″ = 1.92883674304 rad

Height: ha = 14.05112454964
Height: hb = 5.62204981986
Height: hc = 4.68437484988

Median: ma = 16.29441707368
Median: mb = 11.12442977306
Median: mc = 7.03656236397

Inradius: r = 2.16217300764
Circumradius: R = 9.60876892283

Vertex coordinates: A[18; 0] B[0; 0] C[3.75; 4.68437484988]
Centroid: CG[7.25; 1.56112494996]
Coordinates of the circumscribed circle: U[9; -3.36326912299]
Coordinates of the inscribed circle: I[4.5; 2.16217300764]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.8055127661° = 161°48'18″ = 0.31875604293 rad
∠ B' = β' = 128.6822187453° = 128°40'56″ = 0.89656647939 rad
∠ C' = γ' = 69.51326848853° = 69°30'46″ = 1.92883674304 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 = 6+15+18 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-6)(19.5-15)(19.5-18) } ; ; T = sqrt{ 1776.94 } = 42.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 42.15 }{ 6 } = 14.05 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 42.15 }{ 15 } = 5.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 42.15 }{ 18 } = 4.68 ; ;

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**2+18**2-6**2 }{ 2 * 15 * 18 } ) = 18° 11'42" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+18**2-15**2 }{ 2 * 6 * 18 } ) = 51° 19'4" ; ; gamma = 180° - alpha - beta = 180° - 18° 11'42" - 51° 19'4" = 110° 29'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 42.15 }{ 19.5 } = 2.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 18° 11'42" } = 9.61 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 18**2 - 6**2 } }{ 2 } = 16.294 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 6**2 - 15**2 } }{ 2 } = 11.124 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 6**2 - 18**2 } }{ 2 } = 7.036 ; ;
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